Hmm, the barrel jack should also turn the unit on. It should be possible to positively charge the battery over mini-USB, although you might be getting limited to 100mA by USB negotiation with whatever you're plugging it into (more specifically, the Pandora doesn't negotiate anything, so according to the spec, ought to be limited to 100mA) - you'll do best by plugging it into a dumb 2A USB wall wort.
I'll have to get my multimeter out and my (mostly working) Pandora. Mine won't boot up without the battery in (never has), but I can test to see where I can find 5V on the board (looking at the area marked 'don't touch' first of all).