http://en.wikipedia.org/wiki/Digital_artifact:
Hardware malfunction: In computer graphics, visual artifacts may be generated whenever a hardware component such as the processor, memory chip, cabling) malfunctions, etc. causing data corruption. Malfunction may be caused by physical damage, overheating, insufficient voltage (sometimes due to GPU overclocking), etc. Common types of hardware artifacts are texture corruption and T-vertices in 3D graphics, and pixelization in MPEG compressed video.
Software malfunction: Similarly to hardware malfunction, artifacts may be caused by software issues such as bugs in the algorithms, such as decoding/encoding introducing artifacts into audio or video, or a poor pseudo-random number generator would introduce artifacts into statistical research models.
As you can see it isn't a simple "if I have Artifact replace GPU" black and white answer your seeking. It can be "bugs in the algorithms" of the drivers, which normally a updated set of 'working drivers' resolves it, BUT it can be "physical damage, overheating, insufficient voltage (sometimes due to GPU overclocking)," so simply NOT Overclocking resolves the issue, BUT it can be "the processor, memory chip, cabling) malfunctions" so the CPU / MOBO could be going bad and replacing the WHOLE COMPUTER (reuse the GPU in the new PC) would resolve the issue, BUT it could be just the RAM chips are going so buying new RAM would resolve the issue, and so on and so on and so on.
Artifacting is a SYMPTOM of problems and there is multiple solution. The next problem, when analyzing your situation, is any solution would be based on CURRENT or RECENT hardware and software compatible components, your system overall does not qualify. A estimate on individual parts solutions to 'temporary fix' the problem cost MORE (replace GPU, plus PSU, but then maybe the RAM needs to be replaced? (see above ARTIFACTING) does the CPU then cause problems (choking) etc.) over all then simple full solution (replace entire PC).
How to justify the cost for a new PC? That is why I suggested the simplier $395+ upgrade method then say go buy a new ASUS Gamer's Rig, a Dell XPS or Alienware as a solution, to help defer the costs over a short time period, but still provide a least cost solution.