dlbrando,
It looks like perhaps the Macbook will read a music CD but is not geared up to read a music DVD - just like most CD/DVD players, unless they are MP3 players. The MP3 DVDs may not be be transferable.
I checked System Preferences/CDs & DVDs and there are several scroll bars there - none acknowledge what to do for a music DVD, much less a MP3 DVD. Check it out...
You may want to wait and see if you get a better answer here, or you could call Apple and ask them.
Do you have an external hard drive you could copy them to? And then transfer them to the new Macbook? If not, maybe borrow one...
Sorry you're having so much trouble,
Noel