For Sandra Lookingbill of Minatare, Neb., the Veterans Administration benefits system has proven a bureacratic nightmare.

Last December the Lincoln, Neb., VA office turned down her claim for service-connected benefits stemming from the death of her husband. Archie A. McCright, from leukemia in 1968.

Lookingbill who has since remarried, claimed that McCright's illness stemmed from radiation exposure he received during 1937 when he served as a GI in Nevada at atomic weapons tests.

According to the Lincoln VA office, McCright's records "fail" to show any evidence of your late husband . . . having participated in the Nevada tests."

What Lookingbill -- and perhaps even the VA -- did not know was that one month earlier the Pentagon had established through radiation film badge records it possessed that McCright had, in fact, been at the atomic test known as Smoky.

Now, with that knowledge, she is planning to take the regional VA decision to the VA Board of Veterans Appeals in Washington.

But the route ahead of her -- and the hundreds of other potential claiments involved in nuclear tests -- is filled with pitfalls often created by the arbitrary and tightly controlled VA benefits system.

For one thing, neither Lookingbill nor any other VA claimant can pay more than $10 for a lawyer or anyone else to help process a case. That's a law that goes back to the post-Civil War days when Congress feared shysters would get into the war claims business.

For Lookingbill, and the others, it means they must turn to another source for aid. In her case it's the Disabled American Veterans organization which has undertaken a national program to help servicemen and their relatives involved in radiation exposure claim cases.

DAV's national service director, Norman Hartnett, said yesterday his local service representatives around the country have some 125 cases in hand.

But the DAV men are not lawyers. And, as in Lookingbill's case, there often is no personal contact. She, for example, has never met the DAV man in Lincoln who is handling her case. They have only corresponded by mail.

On all VA appeals, the burden of proof is on the claimant to convince the VA board of the merits of each case. Establishing her late husband's presence at the nuclear tests is only the beginning for Lookingbill.

The military records now available show he was with an ordinance company at the Nevada test site Army base, Camp Desert Rock. They also show his film badge recorded no radiation exposure at all.

Lookingbill said recently her husband has told her he drove a wrecker after each atomic test and took from near ground zero the tanks, trucks and other vehicles that had been damaged by the shots.

She also said he had observed several shots.

How Lookingbill can prove her late husband's radiation exposure -- given the zero film badge reading -- remains a problem for both her and her DAV representative. She said yesterday she was told to try to find some of his old Army buddies, but 20 years after his discharge, that's a tough order.

The Army has told Congress some film badges were lost and others not worn.

Sydney J. Shuman, chairman of the Board of Veterans Appeals, said recently that "radiation level is not that important." His group, however, has only approved six radiation test exposure claims out of some 51 cases it has heard.

Claimants, such as Lookingbill, are advised to collect all the service medical records they can in hopes some indication of future illness may have turned up during service.

But many consider that an empty exercise since in fact the slow developing symptoms of leukemia -- cancer of the blood -- don't appear until long after the victim has left the military.

There does not appear to be anything in her late husband's Army record. McCright was discharged in 1958 and worked thereafter as an auto mechanic in Texas.

Nine years after his discharge he fell ill and within a year he was dead of leukemia.

Shortly after his death in 1968, Lookingbill and her two children returned to her home in Nebraska. There she filed an initial claim for death benefits. She was quickly turned down.

At the time she had a letter from McCright's Texas doctor who, knowing of his participation at the Nevada tests, said. "We do not know whether he had enough roentgens [a measure or radiation exposure] at this time to make it a . . . factor" in his illness.

That letter was never used in 1968 but it will be part of the evidence presented at the upcoming appeal.

For Lookingbill and others, the appeal is everything. Unlike any other agency, the VA's Washington appeals board decision cannot by law be taken to the courts.

Precedent from other cases also cannot be used. In fact, only under unusual circumstances does an appeal board decision become public.

Ironically, Carter administration VA officials have already decided they want to change some of the agency's most onerous rules -- prohibition of court appeals and the limitation of $10 on legal aid fees.

But they require new laws and veterans groups, such as the DAV, have been opposing them since changes could cut sharply into their role in the benefit process.

For Lookingbill and others, however right now it is a strange process to gain government benefits they believe they and their chilren deserve.