If your iPod is showing up on your computer there are a number of third party utilities that you can use to retrieve the music files and playlists from your iPod. You'll find that they have varying degrees of functionality and some will transfer movies, videos, photos, podcasts and games as well. Have a look at the web pages and documentation, this is just a small selection of what's available, they are generally quite straightforward. You can also read reviews of some of them here:
Wired News - Rescue Your Stranded Tunes
TuneJack Windows Only
iPod2PC Windows Only
iGadget Windows Only
iDump Windows Only
iRepo Windows Only
iPodRip Mac & Windows
YamiPod Mac and Windows Versions
Music Rescue Mac & Windows
iPodCopy Mac and Windows Versions
There is also a manual method of accessing the iPod's hard drive and copying songs back to iTunes on Windows or a Mac. The procedure is a bit involved and won't recover playlists but if you're interested it's available at this link:
Two-way Street: Moving Music Off the iPod
If you can recover the songs then you'll be in a position to restore your iPod.