After drop, will only boot if connected to power, then boot loop.

After I dropped my iPad, it immediately shut off. The battery was at 54%. Now, it will not power on at all unless it's connected to the external adapter. When connected to power, it will boot, but shortly after the lock screen is shown, it "gracefully" dims the screen to black (like it would after a few minutes of inactivity), but instead of sleeping, it reboots. The battery charge indicator now shows 100%, which is obviously wrong. I have tried the various boot methods - DFU, "Connect To iTunes", etc, but none of this helped. As soon as I unplug from the AC adapter, the device shuts off completely - there doesn't seem to be any power whatsoever coming from the battery.

Before purchasing a new battery, is there a way to determine whether the battery is the problem, perhaps with a multimeter? I am wondering if the connector between the main board and the battery was somehow jarred loose or perhaps broke. Would it be prudent to take it apart, then re-assemble, in hopes that something that came loose would be re-seated? I'd rather not buy a battery only to find out that it doesn't solve the problem.

Any expert advice is welcome. Thanks.