Engine will not restart and run?

OK, first it started with a what seemed to be bad fuel pump problem. We replaced the fuel pump and it seemed to snowball from there. Now our issue is, when you turn the key forward, you will hear some solenoids click and then the fuel injectors will fire and a little fuel will go into the bowls. Turn the key further and it starts, sounds normal? After running for a while under driving conditions or idle conditions, it will die. When you try and restart it, nothing, just cranks. When you check it again, to hear the clicks, no fuel injectors will fire, but you do here other solenoids click. Now, if I unhook the battery and hook back up, the engine starts right up again and goes through the same song and dance. We have replaced the fuel pump, fuel filter, AIC, TPS, Fuel Pump Relay, rebuilt TBI, and we are going to replace the MAP sensor and the Coolant Temp Sensor, just to make sure we have done them all. We need some help here, Sensors are expensive and we are quickly running out of sensors to change. A little history of the truck, my dad has owned it since 2005 and only put 4500 miles on it pulling a camper a couple times a year so sitting all the time has not been very healthy on the truck. When he bought it, it had all of the high performance ignition stuff on it but over the years it has all gone bad so we have switched it back to stock. I am wondering if it may be the Computer since if I unhook the battery it starts up fine again until it dies?