1989 Buick Century Fuel System Problems

Engine Performance problem
1989 Buick Century 6 cyl Front Wheel Drive Automatic

I am having an issue where I am driving and the motor will just cut out as if just shut off. When the problem began to manifest it's self I would be driving down the road and it would act as if the transmission was slipping. (I later found that this was the engine cutting out and then restarting on its own.) It has now gotten to the point where when it cuts out the car will die and it will not start again. However if just let to sit for several hours, you can go and start the car just fine again. As time goes on and I can not figure out the problem, I am getting less and less miles before the car dies again. Now I can only run the car for around 10 miles (20 minuets, city driving) before it dies and will not start. I attributed this to a clogged fuel filter and so I changed it out. However, within the first 20 minuets of driving after the filter change I sadly found that the problem is still there and it was not related to the fuel filter.

On several occasions, while the car will not start, I have verified that there is spark at the spark plugs. I can also hear the fuel pump kick in, build pressure and quit pumping when the system is pressurized. For this reason I do not think that it is the fuel pump. I am leaning to the idea that there is something going on with the fuel injection system. I have no idea how to troubleshoot this. If it is the fuel injection system, then it is not just one injector that is being affected but ALL of them at the same time because I believe that there is NO fuel getting to the motor when I can not start the car. I am also not sure how to get the troublecodes from my car ether.

What sensors/components do I need to look at? What could be causeing this issue. Please help me figure out the problem here.