Did you try moving the folder from the DVD to the corresponding folder on the HDD first?
OTOH, shouldn't the Project file in the Per Project folder include the paths of that particular Project?
Speculating/guessing: could it be SONAR looks for the audio in the HDD folder, but if the Project is opened from the DVD, it gets confused??
"Changing names" of the audio makes me think of backup software, which rename the data in order to be retrieved By the same backup software only. Did you use a backup software or did you just copy the files on the DVD?