Help needed with electrical problem

I have on going problem with a 1997 z24 cavalier. Periodically the car will turn over but not start. When this happens, the relay for the turn siganls will make a buzzing sound. Here recently the fuel pump relay will start doing the same. After the car sets for a while it will start working fine. I have changed both relays and the problems still happens. Some times it will make it a week with out an occurrence then some times it every day. The problem occurs mostly in the mornings. Any advice will be greatly appreciated.

Thanks,

Dan