I never had this problem before, but now if I try to play a video for any of the games, the screen is black but I still hear the sound. What could be wrong?

Codecs I guess. Did you install K-Lite Codec Pack lately by any chance? You may need to configure it if so.

No, what's that? I haven't heard anything about that.

Re installing Adobe Flash Plugin may help

Try this.
Go to this page
1 Right-click in the middle of the video in step 5. Verify whether Flash Player is installed
2 Click Settings
3 Click the left-most tab
4 Uncheck the 'Enable hardware acceleration' checkbox to disable hardware acceleration.
5 Refresh the page

That didn't fix the problem. BTW I hadn't changed it, so hardware acceleration had been enabled, but apparently it always was.

Also, in step 1 it lets me check if Flash is installed and it says I have the latest version.

When I play a video it's black, except if I click at a spot to skip to a certain time, then it shows the image, and goes black again immediately.

I have tried it at different resolutions and both full screen and windowed.

Try to remember what did you change before it happened. New software, updates.. I had similar problem only with ffdshow, easy to fix in configuration panel.

But I didn't do anything at all. Yesterday it worked and today it doesn't.