radio cuts out

This is on an '87 dodge...I bought it used, and the previous owner said that he messed with the electrical system and broke something (he didn't know what). Anyway, the radio is stock. When I open either car door or the glove box, the radio shuts off. When I first start the car, there's a *rapid* beeping noise coming from the dash, and the radio flickers on and off. I know it's from the dash because I disconnected the radio and I still got the beeping. This stops after a couple minutes, then the radio works fine. Except when I open a door or the glove box. The memory from the radio also wipes out whenever the radio shuts off in the above cases. Any suggestions or maybe alternate wirings I could do? Thanks ;)

Sounds like some wires are touching each other, some metal, or there just hooked up wrong