Per a suggestion I found at a couple of forums, I took out the drive and cleaned it with compressed air as well as manually cleaned the lens. It still works the same. So much for the possibly it was that hardware issue. Anyway, I'm a little happy that I was able to do that and manage not to break anything.
I'll think about my options and should it come down to it, I may go buy another drive so I can teh burns again. I'm really not keen on getting any more software, like Nero or anything. And as much as I'd still like to blame Keiko Matsui, I have been burning a lot of stuff to my hard drive over the weeks (I've probably bought more CDs this month than I bought last year), so it could've been a number of people. It still stands that Secret Garden, Matsui, and Crystal Method were the last ones I burned before I couldn't read CD-Rs and DVD-Rs anymore.
At the same time, I'd been getting rings for a while now. And my drive is a wee old. There was something in the HP solutions about reverting my computer to how it was when I bought it, but it's been so many years now I don't think I really want to do that. And at least I know now the problem isn't burning, but recognizing/reading.