It does sound like either the battery connection is bad or there's a problem with the iPAQ's circuit board. If the battery isn't loose, I'd clean the contacts on both the device and battery. You can use a towel paper that's lightly dampened with rubbing alcohol or a pencil eraser. If that doesn't do the trick, then try a hard reset. If that doesn't do the trick either the device itself needs repair or possibly the battery.
-------------------- Lisa Gade Editor in Chief, MobileTechReview