hi
It does sound like the battery doesn't hold any voltage anymore, the battery has most likely completely drained and in a sense died, the battery might be reviveable if hooked up to a charger, not something that a home user would have, so the only thing I can suggest is to replace the battery inside.
I found a video on the replacement of the battery.
(copyright note, I did not produce this video)
http://www.youtube.com/watch?v=BfBRE8osFGQ
The maker of the video sells replacements
http://www.ipods99.com/SearchResults.asp?Cat=21you may be able to find a cheaper replacement from ebay
Just make sure the new battery matches the old one, higher mah is better, same voltage (v) required.
http://shop.ebay.com/?_from=R40&_trksid=p3907.m38.l1313&_nkw=zen+m++battery&_sacat=See-All-Categories