DVD drive will not read DVDs but CDs are fine

My DVD drive will not read DVDs. CDs are fine. When I put a DVD into the drive nothing happens. "My Computer" won't even show that the drive exists when a DVD is in the drive. The computer behaves as if nothing happened. No errors. Nothing. I have to mention there are SOME DVDs that it will read. One movie I tried worked (edit: that DVD movie no longer can be read). but other movies won't, and in particular this one DVD+R data disc I have can't be read. These DVDs work in other PCs.

I have updated all the recommended drivers, uninstalled, reinstalled, etc. I have Windows 7 which is up to date. I have a circa 2012 Dell Inspiron 660s. Here is the info on the DVD drive:

TSSTcorp DVD+-RW SH-216BB