Songs wont play on IPOD

Try using the Restore button in iTunes. This will erase the iPod and restore it back to original settings. Then, instead of syncing it completely, set it to manually manage music and put just a few songs on it. See if they play OK. If that works, add some more. If it works with a few hundred songs, try syncing it again with your normal collection.

Are all the songs your iPod skips purchased once from the iTunes Store?

If so, this is what solved a similar or the same problem for me. The problem is not your iPod but iTunes Store's "Purchased" playlist.

Simply check whether your purchased songs (& videos) are still all inside the "Purchased" playlist. You can find it in the column on the left of the iTunes window. It's ordered under 'STORE' together with the link to the 'iTunes Store' and your 'Shopping Cart'.

If your purchased music is not there than you have to add all your purchased songs/videos from your iTunes Music Library back to the 'Purchased playlist' - just like you would when adding songs to your own playlists.
To find all your purchased files order your library by 'Kind'. All the purchased songs and videos are going to be one of the following file kinds: Protected AAC audio file, Purchased AAC audio file, MPEG-4 video file, Protected MPEG-4 video file.

I hope this solved your problem.

Oh, and of course sync your iPod again then. You might have to delete your iTunes Store music from your iPod first and then sync or maybe even restore the iPod. 🙂