HP-33C repair

[J. Lopez]

I just bought a new old-stock HP-33C from an electronics shop (one of those that prey on tourists). The calc has a great cosmetic look, but it is not working. The rechargeable battery is also dead (I left the calc connected to an AC outlet for more than the five hours recommended in the manual, to no avail). When the machine is turned on (connected to the AC outlet), all display segments light up and remain lit until a key is pressed. Then the display shows one of several "Error #" messages. None of the keys are echoed on the display when pressed.
I would love to have this little calc working and forming part of my RPN-HP collection. Any ideas on what I should do to resuscitate it?
(I always knew that the calc was not working and, even so, I bought it and didn't pay too much. It's just too painful to see such a beautiful piece not working. I would appreciate any feedback.)
Thank you
J. Lopez