If you have display glitches or similar issues in SolidWorks that you suspect may be due to an old driver or unsupported graphics card, there is a pretty simple way to get some good confirmation. It's a setting inside of SolidWorks iteself called "Use Software OpenGL."
Where do you find it? Tools > Options > System > Performance. You will find a setting to turn on Software OpenGL -- it's a check box. Important: You can only set this option when you are in SolidWorks but you have no documents open. Since you're changing how the graphics are being dealt with, if you have documents open in SolidWorks you can't very well make the switch and hence the option checkbox will be grayed out.
Once you set this to "on", you are telling SolidWorks not to use the graphics card for OpenGL functions -- you're essentially bypassing the card. It's not as fast to work in this mode, but if you have an old graphics card, or one that isn't supported, it might be better to work this way. If you're using this setting as part of the troubleshooting process, you'll know that your problem is graphics card or driver related and can proceed accordingly.
BTW, in case you're wondering, we currently recommend the nVidia Quadro FX580 as our baseline graphics card for SolidWorks users.