Residents throughout four Gulf Coast states armed themselves with shovels, rakes, brooms and chain saws today as they were allowed to return home and begin regrouping after Hurricane Elena's massive pounding of their property.

Scattered showers pelted the Mississippi-Louisiana coast line as federal and state officials, surveying damage, found that Elena had left an uneven but wide path of destruction from Tampa to New Orleans.

For miles, the landscape showed broken storefront windows, buildings whose roofs had been ripped away, huge trees snapped as if they were matchsticks. Debris was everywhere.

Officials said complete damage reports probably will not be available for days, but unofficial indications are that Elena caused more than $1 billion in damage, including losses in many areas normally frequented by tourists on the Labor Day holiday weekend.

Red Cross authorities said unofficially that the storm damaged or destroyed more than 17,000 dwellings in Alabama, Louisiana, Florida and Mississippi, where it roared ashore Monday morning after dawdling in the Gulf of Mexico and pelting a wide area with rain and angry surf for four days.

Today, all that remained of Elena, the second major hurricane to hit the Gulf area in six years, were scattered thunderstorms affecting parts of Arkansas, Oklahoma and Texas.

In coastal areas of Mississippi, schools and hundreds of businesses were closed today, and local officials said electricity will not be completely restored for days.

Long lines of automobiles clogged roads next to the few open gasoline stations, and aisles were packed at scattered open supermarkets.

Pascagoula, normally a quiet shipbuilding city of 29,000, was particularly hard hit. Mayor Dale Richardson estimated that 90 percent of businesses suffered severe damage, and few grocery or drug stores and restaurants were open. "It will take a good year for us to get back on our feet again," Richardson said.

One shopping center east of Pascagoula was almost completely destroyed. "We made it through Elena, almost," read a sign outside Toulene Tire Co.

"This county no longer has a commercial center," said Linda C. Rosa, the city economic development director. "We already had an unemployment rate of 17 percent, and the last thing we needed was to have our commercial district wiped out."

Tommy Brodnac, a Jackson County commissioner, said that power is out in the eastern part of the county around Ocean Springs and that it "will probably be three weeks before schools can reopen."

Most of the stately beachfront homes, including the Jefferson Davis shrine, Beauvoir, and motels survived with relatively minor roof damage and broken windows.

U.S. officials surveyed the coastal region to determine if President Reagan should declare it eligible for federal disaster assistance. Gulfport Mayor Leroy Urie estimated that his city suffered $10 million in of damage.

"We took a real economic blow," he said. "I hate to be a pessimist, but I think tourism is dead for the year. Even when we get things cleaned up, people won't come because they know of the mess we've had."

Ingalls Shipbuilding yard, the area's largest employer with 11,500 workers, suffered a "significant amount of damage" and looked like a ghost town. Ten Aegis guided-missile cruisers being built for the Navy there were not damaged, and full operations may resume in a week, officials said.

Scores of small businessmen were far less optimistic.

"It will take a couple of months to get me back in business. I'm still in a state of shock," music store owner Robert Chapman said. "I've got six boys, two of them are working down here and one of them works here sporadically. But, if it wasn't for my kids, I guess I wouldn't open up at all."

Gov. William F. Allain said damage was devastating across Mississippi's coastal areas. "The remarkable thing is, we had no fatalities and very few injuries," he said.

On normally tranquil Dauphin Island near Mobile, residents came back with prayers of thanks on their lips and tears in many eyes. As they saw what Elena had left behind, many recounted memories of Hurricane Frederic, which caused them major problems in 1979.

Like other coastal areas, the small island in Mobile Bay resembled a war zone.

Some of the residents had just completed rebuilding begun after Frederic, which caused an estimated $2.3 billion in damage on the island and elsewhere. They questioned whether life on the island is worth such travail.

"I'm ready to call it quits," said Diedra Gamotis, who said she had begun wallpapering her house last week after finishing repairs blamed on Frederic. "We have been working on this for six years," she said.

"I'm ready to sell this property, buy a bigger house in town and put in a pool," she said.

Compared with her neighbors, Gamotis was lucky. The frame of her house is intact, thanks to reinforcing pylons installed after Frederic. But the interior was littered with broken glass and other debris, and the carpeting appeared ruined by saltwater. A cola machine from a nearby grocery store rested on the front lawn, along with the porch from a neighbor's house across the street.

"You always figure that next time it will hit somebody else," said Lawrence Gamotis, Diedra's father-in-law, who lives two houses away.

His house, and another one he owns nearby, showed the sometimes humorous side to how randomly destructive a hurricane can be. A toilet was discovered in a ditch a few yards from one house, but a small plastic container of nails was found full and intact exactly where it had been before the storm.

"This is a kitchen cabinet -- out of somebody else's kitchen. This barbecue kept standing, and it wasn't even tied down," he said.

Gamotis said he thinks that he can repair both houses within four months, less time than six years ago when the bridge to the island was also wiped out and supplies had to be sent by boat.

Anything salvageable inside destroyed houses on the island must be washed clean of sea water before it rusts and stains. Because running water for the chore is unavailable, residents today began carting huge jugs and buckets of clean water across the bridge from the mainland.

"It's what you call a new decor, courtesy of Elena," Ramona Weaver said. She told a reporter, "You're from Washington, huh? I'm going to move to Washington. They don't have hurricanes there."