Aside from Fanboy attacks, hardware failure is rare. Chances are, the hardware is fine, but the setup is not, for your build.
Although driver reminds shouldn't cause things that you experienced, it does lower the performance of the new card if the uninstallation is not done properly. You probably got more reminds by reinstalling varies versions over and over again, which makes it worst.
download ccleaner, it is free.
uninstall any video card related stuffs.
Reboot in safe mode and delete the associated folders in your drive.
Reboot again to be safe in safe mode.
run ccleaner to clean up the registry, it removes most dead links.
Reboot again in normal and install only the latest driver from ATI.
After that, disable all power saving features on both video card and monitor.
If crashes goes away, then zero in which power saving/downclocking features that are causing problems and start QQ in ATI forum continuously until it is resolved.
If crashes still occurs, disable any special features. If it still crashes, then you may want to update bios. It may not be the bios of your video card that is causing problems, mobo also can cause problems.
If nothing works at this point, you will need google about your configuation to see if this particular setup actually causes problems and see if there is a solution to it. Also call technical support for assistance.
As to the title and others, it is all fine, as most of the poster here are not interested in helping you anyways. You brought a new card, wired and install everything just to find out that it crashes. After hours of fixing it still crashes. Instead of joy you got frustration, and confusion. You should consider yourself "good temper" as I will probably be yelling at tech support 20 minutes after the installation.
Don't unplug anything yet, not until you have no other solutions as it will be a complete waste of time and fluid if the problem is indeed setup. Don't reinstall OS either as your blood pressure will increase significantly by doing so. RMA is not fun, you mail that junk back just so that it will come back to you with a note saying it works fine after several weeks. Keep calm and believe that there is a solution just a few clicks away.
The 2d artifact sounds like a clocking problem, but isn't caused by user. Many ATI user experience problems when the card starts to downclock, or run at lower clockspeed. This is not a rare issue as others will like to believe. ATI engineers may be a bit too aggressive on the down clock and power saving features that cause the video card fail to function properly under some configuration. Some user resolved their problems by increasing the low clock speed.