5 things jump to mind....
HUGE intake leak
It could also be none of the above, but that's where I would start at work, if visual inspection went okay, and computer returned no helpful codes
Any chance you have a check engine
1) as bbunt said.. could be trans - Especially if your RPMs go up before the car will start moving... but I don't see how this would stall the car when you hit the gas.. maybe when you come up to a stop (if lockup clutch is stuck, car would jerk/stall as you come to a stop as trans is locked to motor)
Disconnected or completely dead MAF would act a lot in the same way... and with automatics the engine might not measure the correct amount of load, and cause issues with the transmission (same reason crown vics never shift out of first and will rev to the moon when their fuel pumps fail and they run out of fuel top end..) - that would be where I would start...
3) That or you've got a vacuum leak of epic proportions behind the mass airflow, but your 02 sensors would peg either rich or lean and show
4) Air in, no air out = huge exhaust restriction could act a lot in the same way as a dead MAF - your car would be getting a lot more air and fuel than it could move out.. aside from downstream 02 monitors, best way to check this is use a laser temp gauge, if cat is a LOT hotter on the inlet side than the outlet side when the car is at normal operating temp, then your cat is probably plugged
5) Lack of fuel... see crown vic note in possibility 2.. couldn't hurt to check your fuel pressure, esp as you start to load up the engine, it might be fine at idle but dry up/drop pressure fast as you accelerate
Without actually seeing the vehicle, those are the possibilities that I would consider first off - and if you have a check engine light.. get the codes read, it could point you directly to the issue