Sounds like you have the following problems.
# This seems to be a battery going bad and not able to hold a charge anymore. Try getting another battery or a cheap one off eBay to see if that fixes the problem.
# There is a nick or fault in one of the flex ribbons going from the top portion to the lower portion of the XL. You're going to need to tear the system down and inspect all three ribbons to see which one is faulty or near busted (it could be all three as well). Generally, there will probably be a tiny cut or severe crimp in the ribbon that is causing the system to short out and shut down.
Follow this guide in order to get at the three ribbons: [guide|25070]
Good luck with the inspection and take your time.