let me quote something from your question:
'''"I thought it had died"'''
i think you're right, but you ment that the battery was empty - i think that the battery simply died - as in dead, passed or "moved on" (re-incarnated in a zune battery)
many ipod's are simply dead when the battery dies - the won't be recognized by the computer - as i said - they are dead.
you can order a new battery on ebay - if you order it in china, the will cost around 4$ (tools included).
surely - there is the possibility that there is some othere defect - but replacing the battery is the only thing you can try - everything else would mean to replace the logic board or the whole ipod