Sansa Clip won't power up on battery

Well, if you’re within the warranty period, SanDisk will replace it.  If you’re outside of the warranty period, and want to be able to use the player on battery power, you could try to carefully take the Clip apart (prying the halves apart–people have been able to do it, as discussed in threads here), and then resolder or reaffix using conductive epoxy the loose lead back to the battery.  Perhaps needless-to-say, I would exhaust everything else first.

By the way, did you try to force an MSC connection to your computer (on switch down and locked, and then connect the Clip to your computer while holding the center button down)?  That sometimes seems to fix things, somehow.