car won't start maybe because of aftermarket alarm system?

I have a 96 Accord and at first I thought why it sometimes didnt start was because of a loose battery cable clasp on the pole.. so I trickle charged battery up and determined I sometimes still had the non starting problem. Once, I let it just sit there after a non-start and the next day it started fine. I believe messing with the battery some, which bumpy roads mighta loosened the battery cable maybe?.. may have done something to the alarm system.. sometimes I have all electricity going, radio and so forth, but car wont even budge during ignition; zero happens. I have yanked the controller out for the aftermarket alarm system and still don’t have a start, so I’m wondering what to do further.. thanks!