Mercedes 300E would not start

Hi, I have a 1989 Mercedes 300E. It started fine yesterday morning and I drove it to work (5 miles) headlights on and the heater too, of course (Michigan). I was trying to leave in the afternoon when I noticed the battery is dead. I checked if I left the headlights on but there were off, and the battery terminals are tied. Jump started it, it starts but soon the jumper cable are removed it dies unless I push down on the gas pedal. Done this few times but did not have any luck. I wonder if the battery has an inside short or the Alternator is completely gone wild, or the voltage regulator got bad. Is there a way to test which and diagnose this problem?

Thanks a Million

My guess is that the alternator is bad, causing the battery to drain, so that once you remove the jumper cables there’s no voltage to keep the electronics and ignition working, causing the car to die. You could try taking out the battery and seeing if it’ll accept a charge. If it won’t accept a charge, get a new battery, put it in, and drive straight to a mechanic. If it will accept a charge, put it in then drive straight to a mechanic. Either way have the charging system diagnosed. Otherwise call a tow truck.