IS it just the cursor freezing or the whole PC?
try updating mouse drivers
Overheat due to faulty / blocked fans
Household power surges fridge etc switching on/off
faulty memory stick try memtest http://www.memtest86.com/
virus or spyware scan for both especially if shutting down with in a few minutes of switch on or internet use
driver conflicts especially grahics cards get the latest drivers for your equipment