wireing problem 96 dodge lol

Try a these tests

No 1Check the wiring going to the headlites trace it and check for any frayed or burnt or melted or flaking or bare wires, if that seems to be okay try taking a test probe or meter and checking these wires right back to the source, if the tests all are good then try taking the middle wires on the headlite plug connectors and clipping them off and splicing a new 16 gauge piece of wire from both sockets and grounding them right to the negative battery post terminal or a solid clean fresh chassis ground.

If that fixes the problem when driving and using headlights then buy a wiring harness plastic black tubing from an auto parts outlet and run these new wires through it and use proper o-ring connectors on the wires and use a heat shrink tubing for the wires you spliced and be sure to solder the wires and tie off the harness away from moving parts and any heat sources.

No2 try giving the stereo a whole new fresh solid ground too , plus check the wiring to the radio.

Hope that helps and best of luck.By the way if all posible check the systems affected for current , continuity, and make sure the grounds and positives are a solid feed and when in doubt change the source or feed.Comps is vehicles are very very sensitive devices and can act strangely if an electrical problem exists, plus I've got a strong feeling that some kind of short or weak ground or positive wire is affecting the car's COMPUTER system and bec of that the maincomp=ECM and comp shuts the whole vehicle off.