Welcome to Apple Discussions!
These are general instructions. You may have tried some already. 🙂
Have you played the songs in iTunes for a few seconds? This will authorize them. Now sync your iPod. Do they play?
If not, make sure everything is up to date on your computer...
iTunes
iPod Updater
If that doesn't work, in iTunes, go to advanced-->deauthorize computer. Now play the songs in iTunes. It will ask for your account information (from the iTunes Music Store). Enter that. Now play a few purchased songs for a few seconds. Sync your iPod. Do the songs work now?
If they don't, please post back for more suggestions.
btabz