Computer locks up while playing games

My dad has a windows 7 computer that he made a couple years ago that when playing games like lol and wow the display would start displaying random colored lines or sometimes completely lock up no matter what the graphics were set to or the resolution. When theres graphic card in it says the viideo driver crashed weve tried reinstalling the drivers this happened with both radeon 6570 and 3450 and a 610 gt without a graphic card it still locks up and sometimes has a blue screan of death the computer has a pentium dual core im not sure of the exact model I can check when I get back home and 8 gb ram, the motherboard is msi andit currently has a the radeon 3450 in it but will have the 6570 if the issue is fix able does any one know what the issue could be or what tests we could perform to find out whats causes it sorry for bad editing this was typed on a phone tganks in advance to anyone who tries to help