In control panel - power options - set to "always on". see if that stops the screen going blank.
1. Overheat due to faulty / blocked fans
2. PSU voltages
3. Household power surges fridge etc switching on/off
4. faulty memory stick try memtest click here
5. virus or spyware scan for both especially if shutting down with in a few minutes of switch on or internet use
6. driver conflicts especially grahics cards get the latest drivers for your equipment