The funny thing is, Ive tested the RAM, CPU, Hard Drive all independently. It was doing the Not Responding thing despite all the above, Including re-loading a new fresh OS on a New (and TESTED) Hard Drive.

The only thing I could add to what you said above was to start the machine in SAVE MODE, and see if it happens then. Then try it in SAFE MODE With Networking and compare both safe modes to your normal way of booting.

As your computer restarts - but BEFORE Windows launches, press F8.

To Remember which key to use, recite this little Jingle - (its so dumb and corny, you should never forget it now! ((heh))
Your F8 is in SAFE [mode]; or