Try removing the batteries then replacing. The contacts within the battery compartment are a bit crap at times and the batteries might just be loose. Failing that, try using brand new batteries or an adapter. If those don't work something might have come loose within the GP2X.
Have you considered sticking your cat on eBay to help with the cost of a new GP2X - or better still a Wiz or Caanoo?
I have considered doing so, yet to no avail. Also, the problem is solved, at least in part. only the power cord broke, and thus a new one is needed. Do you know if the Apple Iphone power cord works in the Gp2x f100?