This problem sounds like video memory is set too low. Have you tried adjusting video memory settings?
Enter BIOS of your computer and see if there is an option for Video Configuration, Maximum DVMT (Dynamic Video Memory Technology) settings and set as Maximum.
If above option is not available, check with your motherboard manufacturer if there are tips on increasing the amount of graphics memory for your computer model.
Additionally, try installing the latest graphics drivers here:
You can see below that my system is very similar. I have experienced the same graphics problem or one that is very similar. Intel calls it "video distortion." I get "snow" and moving diagonal lines across the screen. This system does not stay on because it produces BSODs, shuts itself down and reboots, and sometimes runs a CHKDSK on the reboot. It almost never gets to the desktop before crashing. If it does get to the desktop, it will only be there for a few seconds before crashing. No programs or data files have been loaded onto this machine for obvious reasons. I have uninstalled/reinstalled Windows, swapped the keyboard, monitor, and mouse, and uninstalled/reinstalled RAM one module at a time. I do not have a spare LGA 1155 mobo or processor to swap. I have flashed the BIOS and used higher numbered BIOS versions per Intel's instructions. So far, nothing has worked. The issue or issues continue. I do not want a "sort of" solution. I want an absolute solution so that these problems are permanently gone. Please help.
OS: Windows 7 Ultimate 64-bit
Mobo: Intel Executive Series DQ67SW
Processor: Intel i7-2600K
RAM: 4 X Corsair 4GB CMX8GX3M2A1333C9 9-9-9-24. 1.5V
Primary HDD: Seagate Barracuda 7200 1TB ST31000528AS
Secondary HDD: Seagate Barracuda 7200 1TB ST31000528AS
PSU: Rosewill 1000w
Case: Cooler Master HAF 932
Optical Drive: Samsung DVD burner