Well...I don't see a pattern to any of this.
Running the PSU without all systems attachments...proves nothing, IMO. The PSU could still be incapable of powering the full system configuration.
Mouse quirks, IME, are best solved by replacing the mouse. The fact that the mouse freezes when accessing Control Panel...is belied by the fact that you previously accessed CP with no problems.
The fact that the system shuts down...is what I would focus on. No pertinent error messages in Event Viewer? There would not be any if the system is overheating or is underpowered...but there probably would be one if the O/S is flaking out.
How To Use Event Viewer - http://www.bleepingcomputer.com/forums/t/40108/how-to-use-event-viewer/
A CPU failure...or a PSU failure...or a motherboard defect...or a RAM problem...none of these would necessarily provide any clues, if present, although I suspect that a motherboard or RAM problem would result in various STOP errors.