Lumina jerks and occasionally shuts off

Here's the situation. My '92 Lumina Euro jumps when driving it. It makes a jerking motion like it's about to cut off. Sometimes, when I start to break, the car will cut off. Also, while sitting idle it will just die and cut off.
On both occasions, when it cuts off, it will start right back up. I think that it might be an electrical problem because on rare occasions, you can turn the switch to start the car and it will lose all power like it's dead. The radio stations will reset and everything.
While I was driving it today, the speedometer starting acting crazy. When I put my foot on the accelerator, the hand would jump up and go past 85. I was doing no more than 45. Then, when I slowed down, it cut off. I cranked it back up and everything was fine. What's going on?

Here's a list of everything that's been replaced:
Heads redone
MAP sensor
Throttle Position Sensor
Crank Position Sensor
New fuel filter (we initially thought there was water in the gas tank that was causing the jerking)
New ECM

What could be causing this problem. I thought that it was the coil pack until the incident that happened today. This is what I feel is the last hurdle that needs to be cleared on the car before it's perfect. Other than this problem, the car is running better than when it was purchased from my dad's friend.

clean your battery connections and inspect the cables and grounds. if those check out check the alternator for proper charging a failing alternator will do all kinds of wierd electrical crap. also check the ignition switch. if the radio resets it is losing all electrical power so pay very close attention to those battery cables both at the batery and engine block/starter. also make sure none of the body grounds are loose.
good luck with this. oh yeah check the grounds under the dash too and the wires entering the fusebox.

I talked to this guy that my dad knows and he said that it was more than likely the Ignition Control Module (Coil Pack) that was causing the car to do that.

it's possible but my money's on a bad ground. coil pack won't reset the radio. might as well check it anyways they have a tendency to be temperature sensitive when they fail.

Ok, here's what happened tonight. I was driving the car and the jerking was more noticiable this time. When I came to a stop, the car cut off. It had been doing this before so I knew what it was and I put the car in neutral, turn the switch back and tried to crank it again. Nothing happened. I tried it again and nothing happened. So, I put the car in park, turned the car completely off and cranked it again. This time, it cranked right back up. I immediately came back and parked it.
I saw some wires today that were exposed going to the alternator. It was the wires going to the electrical connector that were exposed. Would that cause this problem?

might be. does the battery light come on?? get your charging system checked for proper voltage & current output as well as a diode check. if no problems are found there check the stuff i mentioned before.

I don't remember the battery light coming on. I'm going to put some electrical tape over the exposed wires shortly and see if that solves the problem. If it doesn't, I'm going to check the coils. I didn't see anything else frayed or touching the engine block.

Well, I was on my way home from school this past weekend and the car cut off on me and would not crank back up. So, my dad and I came down Saturday and put the new coils on it. It cranked up and ran for a few minutes.
I got in to drive the car home and about a mile later, it cut off and didn't crank back up. We thought that it might have been the ignition control module so we went to a nearby town to a parts store and got a new control module. We put that on and the car started again. It ran for a few minutes this time then it started acting crazy again after my dad mashed the accelerator one time. It studdered then cut off again. Once again, it wouldn't crank after it cut off. So, we had to go all the way home, get our van and a dolly and pull the car all the way home.
We took it to the guy that told us it was the control module and he's supposed to look at it this week. Anybody have an idea of what it could be? The guy asked me if we had replaced the coolant temperature sensor in it and I told him no. Could it be that sensor going bad? Or is it a wire that's touching the motor?

look somethings causing the car to loose all electrical power intermitently, a sensor or module won't cause this it has to be a loose/corroded wire. since the whole electrical system if affected it has to be something close the the battery. like the ground or main power wire.

Amac, we were both right. I had my control module tested and it was bad. I also had two wires cut. One was under the car near the frame somewhere and the other was going to the ECM.
I came home from school today and I drove my car for the first time since the wires were replaced and I couldn't tell it was running when I stopped at lights. It's running so quiet and smooth. I think it's running better than when it came off car lot.
Now here's a list of everything that has been replaced/fixed:
New ECM
New Control Module and Coil Pack
New Map Sensor
New Crank Sensor
New Throttle Position Sensor
New Platinum tipped spark plugs
New spark plug wires
Heads reworked
Broken wires replaced

This car should be ready for another 212,000 miles!!

Well, I spoke too soon. Amac, since you seem to know everything about these cars, I'm coming to you for help (although it might not do any good because my dad uttered the phrase "junkyard in the morning" when he came and picked it up today).
Anyway, I was driving about 70-75 miles per hour on the interstate. Everything was running fine. All of a sudden, the service engine soon light came on and the car immediately cut off. I immediately got over to the side of the road. I thought that it might have overheated but the light never came on (the light does work, it comes like normal when you are cranking the car and goes out). So, I sat on the side of the road and let it cool down. When I tried to crank it back up, it would act like it was trying to turn over but it would die immediately. A couple of times, it backfired and I could see a small cloud of smoke come from the exhaust pipe.

Amac, do you have any idea what this is?

check the timing belt

I think the loose battery cable was the real culprit because when a battery cable comes loose or loses contact with the battery the alternator puts out spikes in the 30 volt range while trying to stabilize and voltages that high can and do fry the computer, ignition module, and just about anything else expensive in the car and they also make the engine kick and the guages go nuts as the computer goes haywire trying to cope with the voltage spikes. Also the damage from voltage spikes doesn't always show up immediatly sometimes it acts as electrical rust and stuff fails a few days,weeks,or months later and most people dont attribute the failure to the original problem because secondary failures sometimes do happen much later.

I found out what made it cut off the second time.

Apparently, sections of wire insulation going to the crank position sensor had been eaten away by oil (I didn't know oil could do that) from an old/fixed oil leak and the naked section of wire was touching the frame of the car and made it cut off. If I had a picture of the wire that was replaced, you wouldn't believe what you were seeing.
It's a wonder that the car didn't catch on fire. Like I said, I never knew that oil could eat away at the insulation of wires. I have been told since then that it might take some time for it to do it, but oil can eat the insulation.

In a few of the other posts, people are having the same problem and it's the TCC or Torque Converter Clutch. Check out the other posts about the stalling and you'll get a better idea of what to do. I, too, have gone thru replacing so much on my van due to this problem that I've been ready to torch the van and watch it burn... anyway... my money's on the TCC

The problem was solved a few weeks ago. It was some wires touching the frame of the car.