Starts then dies immediately,

I would check for fuel pressure. If it was the security system your security light should be lit.

I assume there's a problem with alternator. Check the grounding to engine, check continuity of a positive wire between alternator and battery. the energizing voltage should be checked as well. Might be the bad connection between battery and vehicle body grounding. Diesel cars are sensitive even in a little loss of connection and rust in the connection points.

See the YouTube video on how to repair broken solder joints on your instrument cluster connector. This takes about an hour and solves a number of intermittent problems. I think it may be under "no start" problems.

Look under the dash by the parking brake and try to see if any wires are being moved or chafed by the parking brake linkages. That is what I have found in the past.

I'd use a gage and check proper fuel pressure, key on engine off. My info says 48 psi.
How long since over-all tune up?

Your vehicle is equipped with the Passlock theft-deterrent system.
Passlock is a passive theft-deterrent systemT. he system is armed once the keyi s removed from the ignition. Passlock enables fuel if the ignition lock cylinderi s turned with a valid key. If a correct key is not used, fuel is disabled.

During normal operation, the THEFT SYSTEM light will go off after the engine is started. Ln the unlikely event that the engine stalls and the THEFT SYSTEM light flashes, wait until the light stopsf lashing before trying to restart the engine. Remember to release thkee y from the START position as soon as the engine starts. If after several tries the vehicle still does not start, the vehicle may need service. At this time, you may also want to check the fuses. See your Pontiac dealer for service.

If the THEFT SYSTEM light comes on while the engine is running, a problem has been detected and the system may need service. See your dealer for service. In an emergency, call the Pontiac Roadside Assistance Program at 1 -800-ROADSIDE or 1-800-762-3743.

This ans other details can find it in this link for 1996 Pontiac Sunfire - Owners Manual.

I hope helps (remember to rate and comment this).

Perhaps the computer is going bad, or the connections to it are bad.

Many lights on the dash are controlled by the computer, including the Service Engine Soon light which should go on when the ignition is turned on as a bulb check feature.

When the car starts and runs under its own power this light should go off and stay off if the emission control systems are in working order.

The service engine light is the check engine light. Different name for the same thing.

Yo man, i have the same bakkie more or less same problem.Lights came on as i was driving on the highway and it just died...pre ecnition...Starts then dies again...bla bla bla.List goes on!
Start by replacing the Petrol pump relay!!!+- R400 i think.

Its next to your right foot ,next to gas pedal.Behind that cover.A small black box!

don't buy it from a dealer!
Good luck

I would take the car to almost any auto parts store and ask them to check the ODB II computer for codes and to reset the "Check engine light". Get the code that they tell you and it should go a long way to pointing you in the right direction to fixing this problem. It might also be that when you pumped the brakes that you somehow set a code in the computer from the ABS system and now that you have the brakes pumped up and working correctly resetting the Check engine light might fix your problem.

Good luck! Write back with any code you get and I'll see if I can help you figure out what the problem might be.