For 17 years, Vikki Moormann has taught in the public schools of Coeur d'Alene, a small Idaho town between the base of a wooded mountain and the shore of a pristine lake. But when she read in the Coeur d'Alene Press last month that Prince George's County was offering new teachers a free month's rent and other incentives, she decided to apply.

"I had no idea where that was . . . . It sounded like a really nice suburb," she said. She went through five atlases before she found a map that showed Upper Marlboro.

But it was something else that prompted the 39-year-old language arts teacher to contemplate moving her family thousands of miles to a place she had never seen: "It was the idea that the community was doing something supportive," she said, because as an underpaid and often unappreciated teacher, "sometimes you just kind of get down."

Since the county's effort to attract teachers drew national publicity last month, more than 2,000 applicants such as Moormann have flooded school officials with calls and letters. In the first week alone, more than 1,000 inquiries were made, school officials said.

"We were rather astounded at the outcome," said David Duvall, personnel officer for the county schools, who heard from Arizona, Maine, Montana and every other corner of the country. "We'll be able to select the cream of the crop."

Through the incentive program, organized by the schools' Advisory Council for Business and Industry, businesses are offering teachers new to the system discounts on loans and meals, a waiver on the annual fee for credit cards, a waiver on apartment security deposits and a free month's rent at certain apartments.

The program is designed to make the county competitive with other jurisdictions as schools vie for teachers in the midst of a national teacher shortage. In Maryland, the state expects that 9,000 new teachers will be needed in the next two years. But only 3,000 potential teachers are exected to graduate from state colleges and universities during that period.

In Prince George's, officials expect that they will need to hire 400 new teachers next school year. But they say that the county is in a good position to attract applicants: In addition to the package of incentives, a recently ratified contract will raise starting pay for teachers from $15,738 annually to $19,000.

Moormann, interviewed by phone, said she imagines Prince George's as a community of opportunity, a place where she might find relief from the frustrations of a depressed economy in her pretty mountain town of 20,000.

Her job there is secure, she said, but if a pending tax levy vote fails, 79 other teachers will be laid off. Her husband recently was forced to leave his job at a sawmill because of back problems and faces few prospects for other employment.

"There's nothing here," she said.

Others wrote to the school board for other reasons:

"I read with great interest an article in the Durham N.C. Morning Herald about Prince George's County needing teachers for the 1986-87 school year," elementary schoolteacher Jane M. Forton wrote. "I am especially interested in P.G. County because I grew up there . . . . My husband is also interested in teaching in P.G. County . . . .

Forton said she sees it as an opportunity to move closer to her parents, who live in University Park. Also, with three years of teaching experience, she makes less now than a starting teacher will earn in the county next year.

"I like where I am now, but I wouldn't mind being around the Washington area because of the cultural advantages there," the 24-year-old teacher said. "I thought that they must take teaching seriously if they're willing to offer that," she said of the month's rent and other benefits.

By last week, school officials had received 2,038 inquiries. They are sending out about 130 application forms daily, five times the number Businesses are offering teachers new to the system discounts on loans and meals . . . a waiver on apartment security deposits and a free month's rent. that went out each day a year ago.

"We had to put extra secretaries on the lines" to receive calls and respond to letters, Duvall said. The bulk of the responses came from outside the Washington area, he said, with large numbers from Pennsylvania, New York, Florida and some western states, mainly Wyoming, Colorado and California.

A school official attending a recruiting event at the University of North Carolina at Chapel Hill said students sought out Prince George's recruiters after hearing about the free rent on a cable television channel.

At a similar recruiting conference this month in Boston, school officials will be accompanied by a pack of county business leaders, who will set up a hospitality suite, hand out apples and otherwise draw attention to Prince George's.

Much of the recruiting effort is aimed at graduating students.

"Money is important to them, for paying back loans," Duvall said. "A month's free rent is worth $400 to $500 . . . . For someone who doesn't have a lot of money [that] is something that would cause interest."

The letters come from students, married couples, persons who have been out of the classroom for a dozen years and teachers with substantial experience.

"My wife and I read an [Associated Press] article in the Port Huron, Mich. newspaper that stated your school system is looking for teachers next year," one letter writer said. "We are looking for an area where both of us may be employed."

The writers express commitment to teaching, and, like all job applicants, speak glowingly of their experience and abilities.

The applicants tactfully omit a need for free rent or any hint that they are looking anxiously for a handout.

"Since I have just completed my student teaching experience, I am enthusiastic about beginning my own teaching career," wrote a senior at Ohio State University. "In addition, I am interested in living in Maryland. I have been there only on three occasions, but what I have seen I like."