1988 Honda Civic Hard starting

Our 1988 Honda Civic has been sitting for about 3 years waiting for us to replace the battery cable. We finally got around to replacing the cable but now we are having problems getting the car started. The starter cranks and the engine wil catch but will instantly die. After doing this 5-10 times while pumping the gas the engine will start and run just fine. When we turn the engine off and try to immediately re-start it it goes through the same problems. We are thinking it could be the following:

1. Old gas. The gas in the car is more than 3 years old. But why would that cause the car not to start?

2. Clogged fuel filter. Sitting for 3 years could have caused the filter to clog

3. Fuel pump. The fact that it will catch but not run every time could be a result of low fuel pressure.

Any thoughts on what is going on here? I have a bet with my wife that it is the fuel filter.