I highly doubt it is the CD-R causing an issue, probably the optical drive.
Is there a good .deb data recovery program someone could recommend to solve this problem?
I would use dd or ddrescue to make an ISO image of the CD-R and mount the image as a drive. If you have a dodgy optical drive, ddrescue should eventually get a bit for bit image. Cleaning the laser with a lens cleaner may help in some cases. Below are the steps I use:
dd if=/dev/hdc of=/home/username/CD.iso bs=2048 conv=notrunc
mount -o loop /home/username/CD.iso /mnt/cd
Then the contents will be available in /mnt/cd, but you're not trying to read from a dodgy drive no more. You can also make the image using a Live CD in someone else's computer onto your 1GB pen drive and mount the image in the pen drive back at the ranch.