So now you can go inside for a look! First push up the docking door and look to see that there is no metal debris shorting out the docking contacts. Verify the battery contacts are clean on both ends of the battery bay. Then remove the four self tapping screws, pull the stylus part way out of the case and use it as a lever to pry open the case halves. When you have it open check the battery contacts, which are soldered into the board, for bad solder joints.

Next look at the supercap, the round thing in the shrinkwrap sleeving. Sometimes they leak, and a conductive crust forms over the narrow insulation ring area, shorting it out. Clean off the crust with a wet swab, dry, and see if it wil boot.

Open up that flex PC connector by pulling the latch to the side, lift out the flex PC cable and check the contacts under magnification, clean if necessary, reassemble and retest.

Don't disassemble further unless all of this fails, it is easy to drop the LCD and wreck it so before popping out the main board get a plush towel or something as a soft landing zone for further exploratory surgery. When you snap out that first PC board things get loose in a hurry. [8D]