It is probably your (IAC) Idle air control valve.

My 1996 Lincoln Towncar will not stay running. When I start it starts and then dies, it will stay started as long as my foot is on the gas. When I release the pedal my car dies. What could cause this to happen?

It is almost certainly your Throttle Position Sensor ("TPS". The Idle Air Control valve ("IAC") generally makes the car run like crap at all speeds. The TPS has more to do with the running of the engine at idle. The TPS on a 1998 4.6 liter V-8 is on the inside of the throttle body. You need to remove the four bolts holding on the throttle body, carefully tilt it up about 1.5 inches so that you can unscrew the two retaining bolts on the TPS. No need to disconnect all of the throttle cables. They will move this far without much trouble. BE VERY CAREFUL NOT TO DROP ANYTHING DOWN THE INTAKE. Remove the old TPS, put the new one on, put the two bolts back in, seat the throttle body, and put the four retaining bolts back in. Plug in the TPS, put the air cleaner back on, and you are done. Start the car and give it a few minutes. It should level out and idle smooth in a few minutes. To test your TPS, by the way, just unplug it. If the car is running well before you unplug the TPS, it will usually die or almost die. If unplugging the TPS has no effect, you can be pretty sure that its no good. By the way, while you are changing the TPS, go ahead and change out the IAC. It is much easier to reach, being on the easy side of the throttle body, and it will almost certainly crap out just after you change the TPS. Mine did. Good luck.

It is almost certainly your Throttle Position Sensor ("TPS". The Idle Air Control valve ("IAC") generally makes the car run like crap at all speeds. The TPS has more to do with the running of the engine at idle. The TPS on a 1998 4.6 liter V-8 is on the inside of the throttle body. You need to remove the four bolts holding on the throttle body, carefully tilt it up about 1.5 inches so that you can unscrew the two retaining bolts on the TPS. No need to disconnect all of the throttle cables. They will move this far without much trouble. BE VERY CAREFUL NOT TO DROP ANYTHING DOWN THE INTAKE. Remove the old TPS, put the new one on, put the two bolts back in, seat the throttle body, and put the four retaining bolts back in. Plug in the TPS, put the air cleaner back on, and you are done. Start the car and give it a few minutes. It should level out and idle smooth in a few minutes. To test your TPS, by the way, just unplug it. If the car is running well before you unplug the TPS, it will usually die or almost die. If unplugging the TPS has no effect, you can be pretty sure that its no good. By the way, while you are changing the TPS, go ahead and change out the IAC. It is much easier to reach, being on the easy side of the throttle body, and it will almost certainly crap out just after you change the TPS. Mine did. Good luck.