Well why don't you leave it plugged in, go to the battery screen and see that it says "charging", then with the device still on at the same screen take the power plug out and see what the thing does.
You could make a backup of your files through active sync or onto a storage card then hard reset, that's what I'd do. Make sure that the device works fine after the hard reset, don't restore the back up right away. Then when things are all clear and it works, if it works, restore the backup and see if it starts doing this again. If so, just do a hard reset and learn to make backups more frequently, and send the backup file you have to McAfee's infected files center and tell them it might have a virus that shows that the battery is completely drained. It sounds like it could be the first virus for the PocketPC (TechMarge...

). Good luck, but it's always good to have a second spare battery anyway.