Kincaid alleged that a subcontractor, Potomac Highlands Support Services of Petersburg, also hasn't been able to secure donated cars.
He said the Grant County group "cannot afford to be involved with any program scrutinized by the Legislature," according to the letter, which the Sunday Gazette-Mail obtained through the Freedom of Information Act.
The foundation switched the name of its donated-car program from "West Virginia Wheels" to "West Virginia Keys" in the wake of the investigation and negative publicity in the media, according to foundation employees.
The group also has started its own internal investigation at the request of AFL-CIO President Jim Bowen. But organization leaders have found no wrongdoing among employees so far, Kincaid said.
"We're not hiding anything," Kincaid said. "If there was something done wrong, I want to know about it."
In his letter, Kincaid also accused an unsuccessful grant applicant, Good News Mountaineer Garage, of waging a "sour-grapes crusade" against the foundation.
Good News Mountaineer Garage of Charleston founded the first donated-car program in the state. Based on its success, West Virginia officials decided to scrap the Wheels lease program and switch to a donated program on Oct. 14.
Good News competed for the new grant but lost by one point to Kincaid's group after a committee reviewed four proposals.
Good News officials acknowledged that they were upset they didn't get the state grant, but they say they are not targeting the Foundation.
"We don't do investigations, and we're not after people," said John Chapman, a Good News board member. "This is tax money. Certainly the government has the right to investigate. I would hope somebody is watching our tax money.
"Frankly, I'm mystified why the state would decide to get out of the lease program because of high costs and give it to somebody who ran a lease program but has no experience with donated cars."
In recent weeks, state legislators have pushed for changes to the new $1 million donated-car program, which ends in July.
The Legislative Oversight Commission on Workforce Investment wants the Department of Health and Human Resources to include other state agencies, such as the Bureau of Employment Programs and the Department of Education, in any plans to provide transportation to welfare recipients.
State Sen. John Unger, D-Jefferson, said that perhaps some welfare recipients should be given vouchers, instead of cars, to boost struggling public transportation systems in West Virginia counties.
He also said adult-education job training programs across the state could make repairs on donated vehicles and are "starving for cars to work on."
"These are the types of collaborations that could save the state a lot of money," Unger said, "and also put in place checks and balances."
To contact staff writers Eric Eyre and Scott Finn, use e-mail or call 348-4869.
Tuesday in The Charleston Gazette: For the amount spent on the Wheels program, participants could have had new cars.