If your Power screen looks like this:
it means the back-up battery is not empty, it's toast.
The back-up battery can be found at the end of the black and red pair of cables.
To get there, you'll need to pluck out the four rubber thingies at the backside of your Axim, remove the four Phillips screws and gently gently pry the unit apart.
However, unless you _have_ a functional back-up battery, which looks like this (except for the burn marks, of course)
there'd be no point in ripping the Axim apart. Send the unit back for an exchange.
If you do have one, you'll need an itty-bitty Phillips screwdriver and very steady hands. First pluck the four rubber thingies from their holes in the back. Unscrew the 4 screws and gently remove the back of the unit.
In the lower right of the second picture, the little white plug that's plugged into the back of the mainboard, and has a red and black pair of wires leading to the /front/ of the board, where the battery is glued into place.
So you have to unscrew a few more screws to loosen the board, twist and pry at the black frame surrounding the PDA a bit (watch for the scroll wheel!) Do not panic when one of the small cables on top snaps loose, those can be "clicked" back on.
Unplug the battery, tie a 5 inch long piece of twine around the plug, pry the battery loose, shake it out towards the center, grab it, untie or cut off string, tie around plug of the new battery and ease the new battery back into place where it belongs.
Re-assemble in reverse order.