Is there output from the head to the amp? The failure of the battery (or what caused that failure) could have taken out the AM/FM head (what you call the 'radio") or it could have taken out the amp.
Either your head unit or amp is bad, you are assuming (is seems) that the fault is in the head (radio), this is not always the case.

I suspect the amp is where the issue is. Have you verified the fuse to the amp? (Fuse 23 in the underhood box, in most model/year variations, check the card in the fuse box lid to be sure.)