Dear Dayle
I have never heard of a mouse/mouse driver causing problems. Have you tried starting DC from another workstation - to eliminate this one being a problem?
The other thing you can check is that the user of this PC did not start running a Screen Saver, as there is a known problem with screen savers producing the same symptoms as you are describing - where DC has seemingly stopped in the middle of a check, or in your case, has not started yet and when the machine is accessed the next morning - that is what the User sees.
Hope this helps.