There is also a small possibility it could be motherboard related. Unfortunately, this is much harder and more expensive to test than a power supply problem so that would probably be your first port of call.

The only thing that concerns me with the power fluctuation argument is that your old PC works fine (to the best of my knowledge) - In general, power supplies have become more tolerant to power spikes and fluctuations. A faulty supply may be more susceptible to changes in voltage though generally with these things, they either work or they don't - There isn't much in between.

If you open your case, are there any lights on your motherboard? Most have at least one to indicate whether there is power getting to the motherboard - If so, then I'm afraid it may be more serious than a faulty PSU.

Let me know what you find - Basically, I want to know if there are any signs of life - Lights, fans spinning up, anything. If not then it's almost certainly the PSU, if there is, then you could be looking at the motherboard as the culprit.