1981 c3 corvette starts but wont go into gear?

I have a 1981 c3 corvette, its got 70000 miles on it, problem is it starts right up and runs strong but the tranny only goes into neutral and park. It sat from 1999 till 2010 outside with a cover on it. Also the fuse box did get wet and alot of fuses are corroded, idk if the tranny is electrical, but could that be the problem?