Sure sounds like a PSU problem
I agree with Bob, this sure sounds like a power supply problem. It wouldn't be a bad idea to check the temps either, since it's so much cheaper and easier to do. I always use SpeedFan, but whatever you use, you should check it. With an Asus mobo I wouldn't think you'd have a capacitor problem, but if you see any leakage around anything on the mobo, that would be a sign. You didn't mention having a graphics card, so I assume you're using integrated graphics. If you do have a graphics card, you want to be sure to disable the integrated graphics in the mobo since they can conflict.