why won't my chevy cavalier start if the battery and starter are both good

could be starter relay

If all it does is click its either a bad battery, bad connection at the battery, bad connection at the starter, blown inline fuse, or the starter needs replaced. There is also a very slight teeny tiny possibility of it being a seized engine.

Dont forget the starter selonoid, but if it clicks then it is the battery.

I had the same problem its crank sensor its only $9 at auto zone :)