98 cavalier won't start sometimes

My girlfriend has a 98 Cavalier 2.2 that will not start sometimes. It'll crank over like it is getting no spark/gas then catch all of a sudden and die after like 2 seconds. After leaving it overnight or for a few hours it will start right up no problem. Also, sometimes a buzzing sound comes from in behind the fuse panel when you release the key while it won't start, like a relay moving or something like that. We replaced the crank sensor, but it was from a junkyard. Any suggestions/solutions would be greatly appreciated. thanks.

maybe try fuelpump relay (under hood on pass. side in fusebox)... sometimes u can switch the fuelpump & a/c relays,just to see if thats it before u buy one (same relay part #)