Does my 2001 Chevrolet Prizm need a new PCM?

My 17 year old son got in his 2001 Chevy Prizm and it wouldn't start. The car tried to turn over and then it just conked out and several attempts of turning over the key in the ignition. I noticed that once the gas pedal was pressed down, the car would just sputter out. It's like the car isn't getting any gas to keep it running! Intinally I was told that it was the Mass Air Flow Sensor because there were big puffs of white smoke coming out of the tailpipe, but after replacing the MAF Sensor, upon turning the key over, the car tried to start, but again it conked out when the gas pedal was pressed on & the battery also went dead! I had the car towed to a auto repair shop and I was told (after doing 2 diagnostic test on the Prizm) that the PCM is going out. I was told that the gas runs through that Fuel pressure system and another fuel line but then it just stops mid point somewhere in the engine. I found a company that has a Remanufactured PCM (already flashed) for $315.00 that I would like to purchase, but I don't know where the PCM is located in the Prizm nor do I know if I can replace it myself. Will it be difficult for me to replace the PCM? I was also asked about the Relay Fuse and possibly changing it out before purchasing the PCM, but again, I don't know where it's located either, nor if that is the problem with the Prizm. Also, all of the lights are working in the car and the bell dings when the key is in the ignigiton too! The Prizm also has a new battery too! Do you think that a new PCM replacement fix my problem? Also, where it the PCM located in the Prizm? Thanks!