Is my graphic card fried?

History: After buying my dimension PC, I installed a brand new graphic card (ATI 9800 PRO) so that I could play more graphically intensive games, keep in mind that I did not replace anything else, so that means no new fan or power supply. Okay so for a while now, certain graphically intensive games end up crashing. games like oblivion and Sims 2: seasons (i assume because of the snow and rain) work fine in the beginning but in the end, it makes the screen go black and my monitor flashes a "NO SIGNAL". From all my tech savy friends, I have deduced that my graphic card is over heating and so in order to preserve itself, it crashes the computer. So now the NEW PROBLEM! I turned on my PC and all of the icons had these weird streaks or lines behind it. It seems as if my graphic card (or my PC?) does not understand shading anymore and so in order to create the illusion of shading, it makes the streaks behind the icon. So in order to remedy this problem, I updated the graphics card and set my PC on "For best performance", lo and behold I get owned! I restart my PC and now during the Windows start up [with the Bar and everything] it had these pale blue pixels going across, and not just like 10 or so, but like a 7 x 20 GRID of them. Moreover, my PC now does not understand scrolling. It moves the page as if they were seperate slides and they move slowly and choppily. And so that's it. So my question to the PC savy folks around here is simply, how do I fix this?