I think I may have resolved it...

It was the Overclock Profile that I had configured with my MSI Afterburner software, for my Radeon HD 5850 card...

I had been sitting here trying to figure what changes had been made to my Video Card drivers at about the time this problem started. This machine is barely a month old, and I started out with the Catalyst 10.3 Drivers.

In fact, the problem started, while I was still using the Catalyst 10.3 drivers, and I didn't bother installing Catalyst 10.4 until a week after 10.4 was originally released, just a few days ago actually when I first installed 10.4.

So...

I had not made any changes to my Vid Drivers, when this problem started. It just seemed to suddenly start one day, for no apparent reason...

But, then I suddenly realized that, shortly before I first noticed the problem, a few days before that, I started setting up several OC Profiles on my MSI Afterburner. Ever since then, I've had my machine booting to Windows with MSI Afterburner automatically clocking my 5850, up to a 5870's stock settings.

I just now opened Afterburner, and reloaded my default profile.

Now Windows Media Player is working just fine!

Interesting!

Now...

If only I can find my Iron Man DVD that seems to have misplaced itself from its case!