2000 Oldsmobile Alero Alero Strange Electrical Problem

Hi, my cousin's car died suddenly; the small-town mechanic she knows found the fuel filter clogged and changed it; did not fix; new fuel pump, did not fix; new battery, did not fix. Here's what it does: jump it off, starts and idles perfectly, everything worksm remove the jumper cabes, the lights including instruments start fading immediately and the engine dies within 10 seconds, then dead, won' t crank, nada, but put the jumper cables back on, and it's back to life. - thought at first it was the PassKey system, now I don,t know. Help! I'm paying!