You may be able to get out of the boot loop with redsn0w.--perhaps put the iPad in defunct mode so it doesn't attempt to light LCD?
Your iPad should be able to power on via an AC charger alone.
You can use a DC power supply to push charge into a battery--but very risky. I have done it before.
I second the idea that this is a dock connector problem--I would start there.
Jessa