So, it was a former rental car and does NOT have AP3 on the glovebox door label? Remote start was stock on most HHRs, unless ordered deleted (until 2010).

 

Welcome to the site

You have already found your problem. You stated that if you tighten the fuse box you loose even more things. This is not normal something has happen to the fuse box and or connections.

You seem to be looking in the right spot just go further.

 

x2 - seems like it's time to remove the upper part of the fuse box, inspect, repair if needed, and reinstall.