I had similar electrical issues last year after installing an aftermarket radio. Granted I will admit that it was my error in judgement that caused my issue, but I learned some things about the electrical system in the process.
The electrical system in our Jeeps goes through a box, referred to as the TIPM. It can be located in the engine bay on the passenger side... most of us would just call it a fuse box, but I learned the hard way that it's more advanced. The TIPM searches the entire electrical system for errors or for something missing. Believe it or not, the radio is something that the TIPM searches for.
You might want to plug the radio back into the harness to see if that would resolve your issue.
Another possible issue could be a good old fashioned bad ground.
I hope that this helps, or at least gets you on the right path.
The worst case would be the TIPM itself...they are know to go bad. A simple Google search and even YouTube videos will prove that.
The important thing is to start with simple solutions, and work up to the more complex/expensive solutions.
I wish you luck.