I would hazzard a guess at possibly the pc is overheating and if this happens the pc will just close down with no warning.
If she is on teh Webcam/MSN and watching Youtube vids this could, depending on system specs, cause the processor to overheat and ultimately cause it to shut down if the upper level temperature threshhold is met.
Opening the side panel of the pc and getting in there with the hoover nozzle taking very big care not to knock it around will take away the dust causing the hot zones.
Remember that your PC needs a solid flow of cold air with a clear zone around the case for air intake. Picture a flow of air coming in from the front and exhausting out the rear of the PC.
My initial guess was an MSN virus however since you never said any strange happenings before shutdown i'm sure its just overheating. Common problem coming into this time of year.