If you go to the Start - Control Panel - System - Hardware (tab) - Device Manager (button) - and look under display adapters it will show you what graphics card you have. It might not tell you the exact brand name but it will give you like Radeon 9600 series which mine is. Then if you go on the google and search it will tell you its from ATI.

For a graphics card its true you don't need to spend $600.00 but you can def get a good one without going crazy either. Its hard to say from what your saying your prob is cause it could be memory related, power, video card, driver or a few other things. That is one of the probs with puters that makes you want to pull your hair out believe me I know from experience. Hopefully you can get this resovled and if a blue screen does come up please write down the code and give to us and we might be able to help you out also.