This will be a tough problem to solve because it is intermittent, and variable. Almost anything could be causing it.
You could test the RAM with memtest86 or memtest86+.
You can test your hard drive with the maker's diagnostic app---though I really doubt the drive is doing it.
You can monitor temps and power outputs with HWMonitor. Unfortunately this is best done for a good baseline before problems arise as HWMonitor may report false readings.
Might install Malwarebytes
and see if it detects anything...don't know what antivirus app you use.
You can check Device Manager for yellow/red flags, System Information>Components for problem devices, check Action Center for Problem Reports, Reliability History and Troubleshooting. This is referring to Win7. If Win8 then I am sure these are present and maybe enhanced and more tools present but may be called something else. SFC /scannow and a repair install can be tried after
backing up drive image.
If this is a maker PC then it is presumably still under warranty. They may also offer remote login tech service.
I just got through checking an old client's PC (Acer E380) with same problem intermittent freezing [I no longer service PCs as it isn't worth people's money with PCs being so cheap but some old clients I will still do as a favor.]. I have test equipment and parts to swap in and testbeds to test parts on. Even then I had to give him a loaner PSU because I could not be certain that was the cause. He has had one freeze since. I also found a swollen cap in the CPU bank and let him know if one is gassing the others will soon follow suit...and that board mush have nearly 60 electrolytic caps. I guess the point is I checked a lot of thinks and still did not feel comfortable with my diagnosis of bad PSU. Likely it was the correct dx, but the one freeze has me gritting my teeth.
He wants the MB replaced. I just sent him my price plus parts for a AM2/DDR2 u-ATX swap (only a single board left at Newegg) or a AM2+/AM3 with DDR3 and used CPU for $85 more or a Intel 1150 setup for only $17 more and roughly double the performance. Running XP which should be interesting to transfer over under a repair EULA. But my guess is he is going to have to replace the PSU as well (Antec Basic 350W running about $30 I suspect). I'd rather see him spend $800 on a new desktop. This seemed like a good one
for what was an emergency, but my PSU got him through a design project for his client so now he has some money maybe he can custom order a good build.