Cross Check,
Air must flow through bleed valve to reach the starter, thus enabling the engine to begin running.
This air could be from APU, gnd cart or even the other engine.
I don't know the -300 system, but in the -200 series the engine bleeds must be ON for start - and it is AC powered, as I said before. That's why you'll be in trouble if you don't have 115VAC (from APU or a gnd cart).
If you have any further question or if my answer wasn't so good (my english is poor, I know, I know...), don't hesitate to ask!
Cheers,
PP