Finally killed an 4HE1 on one here. Definitely the injection pump on ours.
Let's start with yours, though.
There is screen in the top of the water separator mounted by battery, that is overlooked by many. Remove bowl retaining ring and drop bowl and Oring. Now, spin off the diffuser and pull off screen. If it has a steel tank, tank rust can block that screen (happened on many of mine).
It may behoove you to simply remove the separator and place it in a vise. If the retaining ring is seized, you'll have to replace it and know that most aftermarket separators don't have that screen (but, with creativity, you can move the screen over).
Next, once cleaned out, replace engine fuel filter, open bleeder on engine fuel filter and unscrew primer handle and pump till clear of air.
Another killer on mine is the fuel stop. When key is turned on, stop cable must actuate. This cable is independent of throttle cable. The actuator is like a windshield wiper motor, so, at key on, <whir> for a second along with cable movement. Similar <whir> at key off along with cable moving other way.
Final killer is the catalytic converter muffler. If plugged, engine will run up to 10 seconds and peter out. If attempted to restart right, it won't. If left sitting 30 seconds, it will give up to a 10 second run again. Cut muffler to exhaust brake bolts, leave a gap and restart engine. Should prove plugged muffler.