Thank you both for the information. I have ordered a DVD cleaner disk. I had not yet installed the firmware -- so will bypass that.
I'll let you know the results from the cleaning.
I keep wondering if I could copy the files on the DVD using my old computer and put them on a flash drive. Then put the flash drive into the computer with the bad DVD reader and write a data DVD of the files. Would this DVD "play" as a video DVD? Probably not. Anyway, the files are too big (over 4 GB) to bother with copying from the old computer which can read the DVD in question to the new computer which can write DVDs.