If your backup is on an external hard drive or on your network, you should use it, because it’ll be faster than getting it off of your ipod. Not sure what problems you had, but if you can examine the directory and “get properties” (PC) or “get info” (Mac), if the overall size is similar to what’s on your iPod, it’s probably okay. I’d just drag the library into the iTunes window to import them all (that would be without your ratings and playcounts. This will be quicker than pulling the songs from your iPod.
If your backup was onto a small number of CDRs or DVDRs, you could do it a disk at a time unless you think there are too many disks to do without getting tedious.
The least labor-intensive (but possibly most time-consuming) options would be to pull them from your iPod. For Mac, you can use iRip, and for PC you can use iPodRIp, which is now Senuti (which is iTunes spelled backwards). I used it when it was called iPodRip, and it was quick, but that was with a second-generation iPod (ca 2003). Just go to download dot com or versiontracker dot com to search for these, or Google them.
Other apps which I haven’t tried (mentioned on lifehacker dot com):
both of these are for Mac & Windows.