Thanks for the suggestion. It did work, but for someone who knows less than me, there are a few steps to mention.
When it boots into 3.6.8-2, the graphical window hangs. You have to then hit Ctrl-Alt-F2 to get a single-user window to appear. Log in as root, and run "yum install kmod-nvidia".
It is a bit of a nuisance to have to get to a single user window (Ctrl-Alt-F3 would work just as well; Ctrl-Alt-F7 is the graphical window that won't work until you do the kmod).
As noted in my original posting, not all upgrades of the system produce this problem, but somem of them do. Now we have the cure.