unable to sync some old songs to ipod shuffle from new macbook pro itunes

I have an old macbook, a couple iPod shuffles, and a new macbook pro.

I just plugged a *new* (never had songs synced to it yet, though I got it ifor Christmas 2012) iPod shuffle in to my macbook pro and synced a couple playlists.

But when I do so, I get the following error:

Some of the items in the iTunes library, including [xx], were not copied to the iPod "[my iPod name]" because you are not authorized for them on this computer.

To authorize this computer for items purchased from the iTunes Store, chose Store > Authorize This Computer...

I have authorized the MBP, numerous times, and of course every time I authorize it now, I get the "This computer is already authorized" message.

I have seen a few posts advising to try to convert songs to AAC format.

When I attempt this on a song that does not sync to my new iPod shuffle (a song which was purchased in 2007, btw), I get another error message "[xx] could not be converted because protected files cannot be converted to other formats."

What else do you need to know?

I am running OS X 10.8.3, and iTunes 11.0.2 (26).

Thanks in advance for any help you can provide.