Well!
I figure this out well enough. From talking with the folks that use the databases, some of the databases were fine, just a few were slow. Turns out "rebuilding" two of the big ones that the other were looking at fixed it.
A good lesson in FMS rules. I had to open the databases after rebuilding them. It also explained why they weren't backing up to the back up drive successfully.
I dont know, however, what caused it.