Might also be a bad DVD drive. But yea, probably amazon some new DVD's first. They are probably becoming less common in physical stores as optical media dies out. I waffled on tossing out a half full spindle of DVD-R discs and a full spindle of CD-R discs when cleaning out my computer crap last year. Just not sure when I'll ever use them again. Pretty much just use thumb drives and microSD cards now.
Personally, if I was moving disks and changing the OS, I would install the new blank disk and load the new OS directly on that. Afterwards, install the old disk as well, and copy over your data. I recently did exactly that, although it got a little more complicated due to some issues with an LVM2 partition.