Try selecting the AUX input but with nothing hooked up and then turn up the volume.
Do that with engine off and then engine running.
Also lights off and then on.
If you get the noise without audio input then issue is in the amplifier section
If noise only happens with input then issue is in the pre-amp section
"Messing with the radio" means..........what?
Pulled it out and put it back in?
Look up the model number and get the manual, see if there is a "reset to factory" default.
1996 had two stereo options, radio with built-in amplifier or radio with separate amplifier.
Look in engine fuse box for a "JBL" fuse, probably Fuse #1, but not sure they used that in '96, that fuse is for the separate amplifier.
You need to know which one you had from the factory to know where to look for problems with new unit