Fnlowrider, the fact that your engine fires, runs, and dies when fuel is added via the carb means you have a fuel problem. The fact that the motor fires says your ignition side is operating, however, inefficiently that may be. Since you let the car sit, more than likely, fuel evaporated or evaporates from the carb which requires replacement; fuel can also disappear between the carb to the fuel tank depending on how long the car sits. These carbs are old and the gaskets are probably not sealing. If there is fuel in the carb bowls and accelerator pump well, pumping the gas pedal becomes necessary. This action also says a carb rebuild is needed. But you need to decide what you want to do. You have two routes: just get the old gal running in the short term or complete the removal of the ECM + wiring, replace the carb and distributor, and rewire the ignition to function without the computer control setup.
For the short term, to get your EC running again, you need to use the process of elimination to identify the point of where your fuel delivery is being blocked.
1. Look down into the carb and move the throttle as if pressing on the gas pedal. If you see fuel being injected/squirted into the front two barrels, then fuel is being delivered to the carb. If you do not see fuel, then back up to the fuel line at the carb.
2. Disconnect the fuel line at the front of the carb and place a catch container in front of the line, as you (or a helper) turns the key to crank the motor. If fuel shoots out of the fuel line, the blockage is in the carb. If no fuel appears at the end of the fuel line, then back up to the fuel pump.
3. But, before tending to the fuel pump, go back to your gas cap and open it. Listen carefully if you hear any hiss or sounds like that of releasing a vacuum. Sometimes, a bad gas cap especially in hot climates prevents/makes it hard for the fuel pump to suck fuel forward. If you hear a sucking sound, then a vented gas cap is hindering fuel delivery.
4. The likelihood of your fuel line between the pump and carb being clogged is slim but is an easy item to check. Disconnect the fuel line at the pump and carb and blow air into either end. If no blockage exists, then move onto the pump.
5. If further cranking the motor shows no fuel exiting the fuel pump, a fuel pump replacement is likely warranted. Hopefully, this is were your issue lies because the last two: fuel line--between the pump and fuel pick-up and fuel pick up itself--which resides inside the gas tank are a big pain in the butt.
As an aside, the fact the the previous owner did not do a complete removal of the computer-controlled system is troubling because that begs the question of "what else didn't the do?"
Good luck!
