Professional fund-raiser Patrick Koegler was sen tenced Friday to prison for four years and a day for charitable fraud. That was the minimum sentence he could receive because he was on proba tion for a similar offense when the latest crime oc curred. Koegler, 24, was con victed of soliciting money for a talent show for the Ju nior Chamber of Commerce. The Jaycees did not autho rize the solicitation and were not planning a talent show District Judge David Par rish ordered Koegler to make $1,200 restitution to the 35 victims. Koegler was given proba tion in 1985 after he con ducted solicitations for other phony causes. A condition of Koegler’s probation was that he not do any more soliciting. But he had resumed such fraud by April 1987, said Chief Deputy District Attor ney David Zook.