My friend was about to throw out his 80gb Zune because it stopped working. All it would do is faintly show the battery charging symbol on the screen but it wouldn't charge up. I talked him into giving it to me instead of throwing it away and after a bit of research online, I determined it to just be a bad battery. I ordered a replacement battery off of Ebay for $10.50 with free shipping. It took a week to arrive from Hong Kong, but today it arrived in the mail.
In order to do the replacement I needed a T4 Torx screwdriver bit. Lowes had an 8-in-one screwdriver with bits for $6.18 so I was in business.
I followed these tear down instructions for the Zune 80GB which made my job a lot easier. Prying the case apart was the most difficult part of the procedure. Once I got it apart the removal of the old battery and the soldering in of the new battery went quite easy. Though I must point out I've been working with soldering irons for over twenty years so if you've never soldered before you might want to practice on some junk circuit boards before attempting this on your Zune. Here's a photo of the old battery I pulled out of my Zune.
After I soldered the new battery in place, I put the Zune all back together and then plugged it in to charge. It seems to be charging up fine now and is actually usable again.