Josh, A couple of years ago, my wife got into our '93 5.2L and turned the key to start and it did the same thing. The battery had died, so I went to town and got a new one.
When it was installed, same thing: relays clicking, no start, high beams flashing. I tried to disconnect the battery again, pull some fuses and no luck.
After a day of fooling around and calling shops, a dealer service tech told me that because of the security system, I would need to place the key into the 'passengers side door' and lock, then unlock the door to re-set this...............It Worked.
I hope this is all that needs to be done on yours.
PS the little remote control wouldn't do it either
'94 YJ 2.5L/5sp - White Jeep Club #55