It started two days ago:

When I charge the N800 (switched on), the battery status icon on the upper right no longer switches to its animated state but stays at whatever level it had when charging started. When I click on it, though, it says that it's charging.

After a while, it disappears completely. I can still click on the empty space where it used to be and get a message that it's still loading, but the icon is gone.

It re-appears when I unplug the tablet.

This is spooky. Anyone had this before?
Also, I could bet that since this started, battery life decreased drastically (yet again). I'm almost certain I need a new battery now, anyway: the device was used when I bought it and it's almost always on (the original owner bought in in March 2007).

Is there any known connection between the state of the icon and a hardware problem?