1999 mustang will not stay running unless I keep the foot on the gas..?
thats very general...could be the battery, or the throttle body, an O2 sensor, bad gas, leak in the intake/exhaust, water in the engine, bad seals, carbon build up, etc.
Best bet is run the car for a bit (few mins or longer), take it to WOT (redline) if it warms up then see if it fixes itself.
Edit: I see some of the other people have chimed in with part-replacement suggestions. Try running the car first, see if you can get your son to spot any weird things happening. No need to jump to replacing parts without a firm diagnosis on what the problem is, especially in a car that old.