I had my 10 GB touchwheel iPod replaced under warranty a couple months ago. Similar problem.
When the remote was plugged in, and twisted, a short would hard restart the ipod. If you twisted it again while it was restarting, it would give the low-battery icon and fail to respond until it was plugged into a computer.
The hard restart reset all settings (time, soundcheck, EQ, contrast), but didn't wipe out any files.
Oddly enough, my remote caused other iPods to short, AND other remotes caused my iPod to fail. Genius bar at Clarendon had never seen it before. Sent it off to Apple. They had no problem reproducing the error and had a new one to me in two days.
Good luck.
-atomium