Same problem here with the Touchstone and my Touchpad.
Amazing! Thanks for the tip on tapping the back!
I did it lightly while the Touchpad was on the Touchstone and I could
see the message and lightning bolt on the battery repeatedly occur.
I didn't stay on however. So I pressed on the back of the Touchpad
while on the Touchstone and now the lightning bolt is on. I doubt it
will last more than this one charge, so jason.hamilton is probably
right that it's a loose internal wire.
I really don't want to return my Touchpad to HP, so if I can find a good
guide showing how to open my device without damaging it, I'll probably
crack it open to take a peek.
This guide is pretty good:
HP TouchPad Repair Manual - iFixit
Though they warn you right from the start you will probably break the
clips anchoring the front panel to the rear case.