iPod batteries die -- we all know that. Generally about two to three years after you start using them (depending on the intensity of your use), the battery will no longer hold a charge for long, if at all. Batteries can be replaced, of course, but it's not necessarily a simple procedure, and it might not be worth it on an older, smaller-capacity iPod.
I've written an article explaining some ways to use the iPod after the battery dies, assuming you don't want to try to replace the battery. To sum up, you can use it to provide music as long as it gets power (from a car, or from an AC adapter); you can use it as a source for iTunes on any computer; or you can use it as a hard disk for backups, providing you with a pocket-sized backup drive that you can shuttle between home and office. More details are available in the article.
Mac OS X Hints
http://hints.macworld.com/article.php?story=20060629010654178