this usually happens when i try to start it in the morning...sometimes it will start for a second then immediately die, sometimes it just doesn't start at all, and it takes a few turns of the key before it finally turns over...anybody have any idea why it might do that?...it's an '84 z28...

 

Presuming this is NOT a CFI engine, check the choke linkage, high idle linkage, and choke heater. Clean and lube the linkage if you aren't sure when it was done last.