Two things I know for sure, being a long time fan of the game. As you probably already know, Diablo 2 out of the box only supports 640x480, and with LOD came the ability to run 800x600.
The issue: As of Vista, it's real buggy with software D3D. Diablo II will try to launch in software D3D mode, many never get the game to work because of this. You may already be aware, it will not run under Vista or 7 like this, however upon installation it should show the "detected video devices" or something similar, be sure to choose the "hardware" option, and then the game will work. Again, you may already know this.
However, sometimes even the slightest change in your system or the game itself can cause it to revert to software. In the program files list, in the tree you'll see the video setup executable, run this, verify you're using hardware acceleration, then try to run it.
You may know all of this, and I think it's likely this isn't the issue, but gotta address that first since it's the biggest hurdle for any D2 players on Vista/7.
As far as what you describe, I can't imagine what would cause it to do that.. I guess you could try pressing Alt+Enter while playing, and see if that brings it full screen. Otherwise, have you tried manually setting the resolution back to 640x480, then back up to 800x600? What you're describing sounds like the game itself, not the display or any part of Windows.
This usually happens when the resolution to draw is lower than what the program can or is displaying, most often I see this with Emulators. Maybe I'm over thinking it.
Were you running it windowed? -w?
