Not true. Hoover and Taft did not serve in the military, nor did they hold elective office before being President.
President Taft was on the Ohio Supreme Court, appointed Solicitor General of the United States and was a judge on the United States Court of Appeals for the Sixth Circuit, as well as Governor-General of the Philippines and President Hoover was Secretary of Commerce, but I take your point. Mr. Cain has NEVER held a government office. The Federal Reserve is not a government operation.