It's a puzzle and that's no doubt.
It is always much harder to diagnose a problem at distance but I am forced to admit to a lot of head scratching here.
I would suggest trying a basic mouse & keyboard just to totally eliminate the Logitech ones as the cause of the problem as there have been occasional issues with Logitech before.
If that doesn't work then try the different Graphics Card.
If that doesn't work try a different monitor. (Sounds stupid but we have had a couple of problems on the forum recently that were due to incompatible monitors)
I'll keep thinking and I'm sure Dark Mantis will offer further advice and/or moral support.