An iPod doesn't "authorize" to an iTunes Store account, per se, it's linked to a particular iTunes library. You can't prevent someone from playing any tracks that were on the iPod, but they won't be able to transfer those tracks to iTunes and play them without being able to authorize to your iTunes Store account which they won't be able to do.
As to your second question, you cannot yourself deauthorize a computer that's not working or to which you no longer have access. You can authorize a total of up to five systems, so it's probably not really important that you deauthorize your dead unit now. Once you reach five total authorizations, a button will appear in your iTunes Store account that will allow you to deauthorize all your systems, so that would at that time recover the now-useless authorization.
You might want to change your iTunes Store account password, just as a precaution, if you didn't erase all the data on your old computer before you sold it.
