Help with a troublesome Mini

[Ashapalan]

The hardware in question is a 1st generation 4gb ipod mini.

The unit is currently (and has been for some time (a day)) turning itself on and off, getting as far as the apple icon before 'rebooting'.

I have tried the following...
reset with menu and play button
plugging into computer to reformat - computer hasn't recognized, including with the recent updater.

I have healed a few ipods in the past but this one has me stumped, and if it carries on doing this 'boot dance' any longer i fear that the hardrive will break.

Does anyone have any suggestions as to how to fix the problem?
thank you for your time.

edit...

further resetting attemps have altered the ball game. The unit is now stuck on the low battery icon, regardless of being previously fully charged...

is it possible for an ipod battery to die 'all at once'?

2nd edit

okay, back with the original problem now.