1997 TransSport engine and starter problem

As daughter was driving down the highway to work the other day, the engine started to loose power and died on her. When I got there, I tried to start it. It would crank over and start, but ran extremely rough and died right away. I could start it again, but it would only keep running (very roughly) if I kept pumping the gas pedal. As soon as I stopped pumping the gas, it would die.
After doing this a few times, the battery would not turn the engine over anymore. I tried to jump start it with my truck, but it still would not crank the engine over. I recharged the battery, but it still will not crank the engine. When the ignition key is turned on, the solenoid on the starter engages, but that's it. Sometimes the engine will crank over slightly, but nothing more.
Hoping the battery was bad, I changed it with the battery from my truck. It did the same thing, the solenoid clicked. I am guessing that my starter is bad, or a ground somewhere.
None the less, after I fix my "starter" problem, I am sure that I will still have the original problem of the engine not running without pumping the throttle. Any guesses?

YES for "a ground somewhere". A lot or weirdies happening altogether on a sudden lets me think of an electrical problem...like a corroded ground. I"d check main battery cables, at both ends, + and ground...and I'd run some more grounds between firewall and engine. At least this would eliminate this pissibility . ALl those components -starter, injection, battery, cannot die all at same time; make some voltage measurements with headlights ON, between battery poles, then battery+ and engine block, then engine block and body ...that may reveal interesting things. THen with someone trying to start, measure between engine block and car body...voltage should stay at zero...if a few volts show, some bad ground exists.

a quick check for bad engine and starter grounds is to check for voltage on the coolant. with the ignition in the run position take a volt meter and put the positive probe in the coolant (cold engine) and the neg on the battery negative pole. anything more than .03 volts indicates bad grounds.