Diane Smith, a clerk-typist for a Southeast Washington agency that tries to find new homes for displaced low-income families, recently became one of her own clients after an accidental fire drove her and her four children out of their three-bedroom apartment and into the ranks of the homeless.

Now she is one of hundreds of fierce competitors in search of Washington's scarcest commodity -- a low-cost home they like and can afford.

"I had a small inkling of what the housing market was like . . . but I never realized how desperate the need is for low- and moderate-income housing," she said. "I wonder what low-income people are supposed to do."

Her agency, Far East Community Services Inc., has tried to help with no success. The city housing department has nothing to offer but waiting lists. She has spent each weekend since the fire two months ago poring over the newspaper ads, calling landlords and visiting more than 25 apartment developments throughout the District and Prince George's County.

But she has found only frustration, despair and discrimination against her children, she says. In the meantime she has doubled up with her parents and a brother who live in a two-bedroom house in Southeast. She and her two daughters sleep in the basement on a hideaway bed and her two sons share the brother's bedroom.

According to city housing officials Smith, who earns about $8,400 a year, is one of a growing number of city residents, many of whom are single mothers earning less than $10,000 a year, who can no longer afford private housing in the District. The average rent in the city last year was $230 a month and the average price of a new home is $97,000. The major alternative for such house seekers is public housing or subsidized projects. But there, waiting lists are lengthy because vacancies are rare.

"We have a shortage of affordable housing," said James E. Clay, deputy director of the city's housing department, which has 7,500 families on its waiting list for public housing and 2,000 more families waiting for a federal rent subsidy.

"Even if she [Smith] pays 25 percent of her income [$175] she will have a difficult time finding a three-bedroom apartment she can afford. Clearly we have a problem," Clay said.

Smith says she usually tells private landlords the size apartment she needs but then points out that she can afford to pay no more than $250 a month. Sometimes the landlords laugh, she said, "and tell me there is nothing available at that price," the small, 30-year-old woman said.

She has discovered, she said, that the average rent for a three-bedroom apartment is at least $300 a month and "that's not counting utilities . . . . In a two-week period, I don't bring $300 home after deductions."

And she faces discrimination against her children, she contends. "Some of them [landlords and management companies] have hung up on me when I tell them how many kids I have," she said.

Margaret Myers, a city housing counselor who is trying to help Smith, confirmed that there is still discrimination against children, although a city law makes it illegal.

"I don't care how much money you have, eight out of 10 chances, they [owners and landlords] won't take you with children," said Myers.

Before the Aug. 31 fire, Smith and her family lived in a subsidized apartment at 5111 Fitch St. SE, and paid $173 a month rent plus utilities, she said. But H.G. Smithy, which manages her former building, has left her apartment boarded up and unrepaired while the company settles with its insurance company.

Martin Johnson, the property manager for the building, said tenants who are burned out are usually transferred to other units but none were available. He added that Smith had failed to stay in touch with the company after the fire. She denied that and said she was told the company refused to rent to her, an allegation that Johnson denied.

After the fire Smith had thought that maybe she could move her children, who range in age from 9 to 14, to a better neighborhood, away from drugs and gambling.

But one foray into the city's housing market quickly changed her mind about that, she said. During her two-month-old search she has only found one vacant three-bedcroom apartment and that rented for $350 a month without utilities, she said.

"I just have to keep hoping that there will be someone sympathetic enough to realize my plight, that I am in a desperate situation," she said recently. "Prayers are all I have . . . that someone will take a chance on me."