W124, Used Parts Assortment

About 2 months ago my wife took the car to exercise class and when she came out to come home and started the car it backfired and would not re-start. I checked it out the following day and though it didn't backfire it would not run for more than 1/2 a second. I had the vehicle towed to my house and have periodically tried to start it with the same result. It will fire, run for about 1/2 a second than shut off. It will continue to do that until I depress the accelerator pedal then it won't start at all.