you'll need a very high amperage bench top power supply if you want to run the gun off it, i have a 7 amp adjustable one and the overload led lights as soon as i press the trigger... id say minimum 15 amps, and wtf it must be a very old car battery to be drained like that by a airsoft gun! i know car batteries arent made for deep discharge purpose but still...
and for hooking it up to the wall just buy 4 big diodes make a bridge with them (to obtain dc) and watch you gun firing it's last round with an incredible trigger response