Shattered by war and forgotten by the world in a rush of fresher crises, southern Lebanon has nonetheless become a magnet that refuses to let go of those it attracts. Palestinian guerrillas, Lebanese militia, Syrian forces, Israelis and U.N. troops have, in turn, been drawn into its harsh hills and none have found a way to take their leave.

While guns have been quiet on Israel's other borders since the 1973 war, they have continued to destroy life and property along the frontier with Lebanon.

So fatalistic have southerners become that often even artillery barrages will not send them scampering. In the port city of Tyre, controlled by the Palestinian guerrillas and their leftist Lebanese allies, residents have grown so accustomed to shelling from the Israelis and their right-wing Lebanese allies that they ponder the day of the week before fleeing:

If it is Monday, more often than not they will tough it out rather than lose a week of school and commerce. But if the trouble starts on a Thursday, they are more likely to load their valuables into a car or pickup truck and head north.

Numbed by the moral, material and human damage sustained in southern Lebanon in the past half decade of civil war, invasion and factional strife, peasants and soldiers, politicians and diplomats now look to the United States for a solution to a problem so complicated as to defy rational analysis.

President Reagan's name is constantly invoked in ruined Lebanese villages and elegant embassies and his possible role debated by Israeli generals, their Palestinian guerrilla foes and U.N. peacekeeping commanders trying to keep them apart.

There is no common denominator to such talk except for the slim, even improbable hope that if the new U.S. president is serious about reasserting American greatness, he will somehow bring order out of chaos here as a first step toward a Middle East peace settlement. Even if it is not on his own agenda, Secretary of State Alexander M. Haig, Jr. will find his Arab hosts compelled to bring up Lebanon's forgotten war when he visits the region early next month.

Now the battleground for the Arab world's own warring states as well as Israel's struggle against the Palestine Liberation Organization, southern Lebanon seems caught up in often contradictory currents. The required trade-offs to achieve a solution appear so vulnerable to the slightest upset that southern Lebanon is on no one's list of top priorities, with the possible exception of Lebanon's own beleaguered and divided government.

Even many of the southern Lebanese, the faceless victims of a relentless struggle not limited to just Israel and the Palestinians, have stopped caring. But they, along with all the other parties to the conflict, are convinced -- or at least say they are -- that the United States holds the key if any solution does exist.

The little world they all say they want ordered -- but only their own, often mutually exclusive terms -- is without reliable statistics or straight answers.

It is also a world without a modicum of safety or central government authority despite -- or rather because of -- the myriad armies, both domestic and foreign, occupying its territory. For all practical purposes, there is no government south of the Litani River. The tasks usually carried out by a government -- supplying water, generating electricity, caring for the sick -- are being done by UNICEF, the U.N. Children's Emergency Fund.

Southern Lebanon's tragedy is a product of both Lebanon's devastating 1975-76 civil war and the broader Israeli-Arab conflict. The collapse of the governing authority of the central government in Beirut left a vacuum in the sensitive region that quickly made it an arena for warring and posturing by a half dozen of the Middle East's most prominent belligerents.

This four-part report will examine southern Lebanon, looking at the region itself and the roles of the Israelis, the Palestinians, the Lebanese militias, the United States and the U.N. peacekeeping forces.

The most comprehensive estimate of the physical damage wrought in southern Lebanon from 1969 to 1978 -- when a massive firepower invasion was launched by Israelis using U.S.-supplied weapons -- was made in the U.N. special economic and disaster relief assistance report published last October.

"Ten thousand houses were totally destroyed and 46,000 damaged; 85 percent of the villages are no longer linked to any water supply system," it noted.

"The electricity network was destroyed by shelling, with the result that 64 percent of the villages are short of electricity or have none at all. Postal, telegraphic and telephone services are no longer available or inadequate in about 82 percent of the villages.

"The local network of roads is badly in need of repairs," the report said."Poor communications, in turn, impede the restoration and development of the local market and normal economic relations between villages and with major towns.

"Economic activity, which was declining even before the war, has come to a virtual standstill in many parts of the region," the report said. "Agricultural production received a setback due to the destruction or abandonment of orchards, farms and tobacco plantations. The animal population has been reduced. Small industries were severly damaged by the war and subsequently have shifted to large cities or have stopped functioning."

If anything, the reality is gloomier than the report indicates. Its chief author privately noted that it covered the entire southern province of Lebanon, whose northern stretches remain largely intact.

Nor does the report mention the dislocations brought about by wave after wave of southern refugees who have fled the war zone, often to become unemployed, turbulent squatters in Beirut, Sidon and other Lebanese cities and their suburbs.

No one knows how many southerners have left -- or how many have returned. Haim Fayad, governor of the southern area of Lebanon, estimated conservatively that at least 100,000 southerners remain displaced.

The civilian casualty toll is also unknown and such is the breakdown of the state that even the gendarmerie's official statistics are based in part on newspaper clippings.

But even taking into account government exaggertion, about 1,000 Lebanese civilians are thought to have been killed in the 1978 invasion alone, when the Red Cross estimated that nearly 250,000 of the 300,000 residents of the south -- just under 10 percent of Lebanon's population -- fled north. An Arab League report said 309 civilians had been killed and 1,011 others wounded in southern Lebanon between July and the end of September 1979.

Especially distressing is the situation in southern schools -- 165 have been destroyed or damaged -- and hospitals, where, except for relatively secure Sidon, there is practically no adequate care.

The south is so depleted of competent administrators that Lebanon is hard pressed to allocate, much less spend, the $2 billion earmarked by Arab countries over the next five years for southern reconstruction and development.

Tyre and Nabatiyah, Palestinian-controlled cities and favorite targets for Israeli gunners and those of Israeli-supported Lebanese Christian troops under Maj. Saad Haddad, are full of shuttered shops and holed walls. Yet the countryside is studded with new houses that have sprung up as the Lebanese have taken advantage of the anarchy to build without official permits.

After the invasion, many southerners returned to their villages: for the most part they were the old, the very young, the women and the poor unable to afford city prices. The rest have sought safety and their fortunes out of harm's way in Sidon, Beirut or abroad.

In classic Catch-22 style the various armies now provide a major source of gainful employment for most of those who have remained. The few others still there are farmers brave enough to work their dangerously exposed land and a thousand or so civil servants paid to stay put, but unable or unwilling to carry out their tasks for the central government.

Since they can make more money working for the U.N. forces, few southern Lebanese cross to Israel to work any more, although many did when Israel began its "Good Fence" limited open-door policy in 1976.

In Tyre, gunslinging for one of the many National Front militias can pay as much as $330 a month plus a cut in the otherwise moribund port's smuggling activities.

In an effort to restore basic services, generate economic activity and redirect loyalties to Beirut, the central government has entrusted UNICEF with carrying out $47 million worth of health, school, water and power projects this year.

UNICEF is administering the funds, donated by Arab countries, because the Beirut authorities have no noticeable authority in "Haddadland" and only a little more in the U.N. area and the regions immediately north.

Fayad, the southern Lebanon governor, said in an interview in Sidon that while Lebanon countries to pay the wages of those public employes who have remained in the south, it has refused to send more gendarmes or other civil servants "because the area in our eyes is under effective Israeli control."

Nonetheless, he said, "We want the Lebanese living under the Israelis to know the state has not forgotten them, and UNICEF can move more easily in the enclave."

Theoretically, a group called the Council of the South, set up by Lebanon in 1970, should be in charge of rehabilitation there but it has been paralyzed by a combination of inefficiency and corruption.

Thus while the council bickers about restoring roads and buildings, UNICEF is putting piped running water back into the area for the first time in four years and is extending power lines from the palestinian-controlled area north of the Litani River and restoring schools damaged or destroyed by the fighting.

All parties have agreed to let UNICEF carry out this program. Yet most observers are pessimistic about whether it can accomplish much, given the atmosphere of hostility and violence and absence of governing authority.

Haddad, for example, has more than once, shelled the Palestinian stronghold of Nabatiyah to underline his unhappiness over matters such as the cutoff of his electricity.

Contradictions abound when it comes to the motives and actions of the principal players in the south.

Israel claims Haddad is a free agent. The Palestine Liberation Organization -- especially its major faction, Fatah -- insists that some of its members are similarly hard to keep in line. Particularly recalcitrant are the Iraqi Baath Party in the National Movement and its Palestinian counterpart, the Arab Liberation Front.

Perhaps significantly, the only Palestinian operation that succeeded last year in breaching Israel's security fences and attacking a settlement was carried out by the Arab Liberation Front against the Misgav Am border kibbutz. Fatah officials privately decried the attack, although in public they felt obliged to praise it.

Their contention is that armed struggle may still be the official PLO policy, largely for purposes of internal consumption, but diplomacy stands a much better chance of achieving results.

Yet, even this Palestinian circumspection is open to question. Officially, Palestinian military commanders in the south admit Israeli preemptive strikes have put them at a disadvantage in their main task of protecting overall leader Yasser Arafat's basically political operation in and around Beirut.

In recent months, Haddad and Israel have fired less and the Palestinians relatively more, but the ratio is still better than 2-to-1 in favor of the former, according to U.N. estimates.

U.N. officials who note the increasing Palestinian aggression since November wonder whether this new policy reflects tensions within the leadership or efforts to get the Palestinian question back in the limelight after the Soviet invasion of Afghanistan, the Iranian-Iraqi war and other such distractions.

Some diplomats argue that fulfilling the U.N. mandate and removng Haddad and other Israeli interference in the border area is a prerequisite for a settlement of the Palestinian problem on the West Bank and the Gaza Strip.

The Lebanese civil war was brought to a formal end by the Arab world, which was able to do so precisely because Israel was not involved. Syria, these diplomats argue, would not consider joining the peace process until the Israelis were out of Lebanon and no longer poised as a permanent destabilizing threat there.

Lebanese Foreign Minister Fuad Boutros, in an interview, insisted that the United States is "directly responsible for what happens, for that is the price of being a superpower." That he defined as the obligation to "deal with several hot spots at the same time."

Like many other observers, he argues that the U.N. peacekeeping force's presence "has all but sunk into oblivion" and that the international force "has only one mission: to freeze the situation and maintain the status quo."