OH MY GOD!! I had this exact same problem with an HP laptop.
To me it was one of the most amazing issues I've ever seen. So amazing I made a youtube video of it!
http://www.youtube.com/watch?v=ixGIfBrW5wM(Laptop shown running WinUAE then in Windows)
It's not a monitor issue. When you twist the motherboard portion it "pauses" the entire computer system.
I tested it several ways. First, I would twist it a little and get it to freeze, then I would leave it frozen for a few minutes and then twist it back to unfreeze it and the clock would stay several minutes behind.
I tried rendering, would twist to freeze the system, wait a several minutes, then unfreeze it and the render continued exactly where it left off.
Tried with downloads too. Started to download a file that would take aprox. 30 seconds, would 'freeze' the system for about 5 minutes, then unfreeze and the download would continue right where it left off ( wish I had tested this part more)
At one point I had left it frozen for several hours, twisted it to unfreeze it and the clock was several hours behind.
Unfortunantly it was a relatives Laptop and I never got to disassemble it. (They just bought a new one)
I thought that it would be awesome to figure out how this AMAZING fault worked and create a "PAUSE" button for my desktop.
I was amazed that the everything could be paused for so long, have no memory corruption after several hours, and seem to pick up on the next CPU cycle it left off on.
Pretty crazy. I never thought I'd see a similar issue again.