The running and die problem, could be a plugged fuel filter, but gas today is so clean. I would still swap it out.
Next up would be the fuel pressure regulator. Common issue on isuzu's with over 100k on them.
The starting problem could be, as you state, bad battery connections (clean up the battery posts) and then you could swap out the starter.
a bad starter typically will turn over very slowly, or you hear a click in the starter solenoid and then nothing ....