1988 Chevy Nova car won't start

I have this "mystery" problem with my 88 nova. The problem is that after i drive my car to where i need to go, it wo't start when i try to turn it on again. The car won't turn over, i don't hear any clicking noises wheni turn the key, i have full lights, and they DON'T dim, so it's not the battery, you CAN jump it as long as it's car to car and not car to jump box, i just recently put a new starter in and that didn't really solve anything, anyadvice or if you have a solution i would be very grateful

-David Capano