Most iPod troubles are due to dropping the iPod. This causes the hard drive to go out of alignment and therefore require more juice to spin the drive. More juice than the battery is designed to provide. This, then, appears as a battery issue.
The way to test whether you have a bad battery or a bad hard drive is to use the Repeat One and the Repeat All settings. Do two different battery tests. You fully charge the iPod and restore it before these tests, and you turn off shuffle and backlight.
The first test: Repeat All. If the iPod plays for many hours on this setting, then your hard drive and battery are fine.
The second test: Repeat One. If the iPod plays for a very short time, it is either the hard drive or battery. In this case, do the Repeat All again. If the iPod does not last long, then you have a bad battery.
Hopefully that makes sense!
Basically, the Repeat All will isolate the hard drive, because it has to keep spinning the drive to find all the songs, whereas the Repeat One caches the current song and does not require the spinning of the disk.
Good luck with your iPod. For best results, don't drop the iPod, get AppleCare, and restore the iPod every month or so.