88 Seville radio works w/dead battery on jumpers only

I have this odd problem with an 88 Seville I bought. The stereo does not turn on, background lighting from the internal lights works but nothing else. Had car sit for a month and battery went dead. Went to jumpstart the car and the stereo was working when we put the jumpers on! All excited, jumped car, stereo again not working (it sounded pretty good for an 18 yr old system). Any help would be appreciated. Checked all the fuses and realys, everything in the darn car works fine except the radio.:banghead: