The PSU in her system is a PC Power and Cooling from their industrial line before they got bought. This PSU pushed a GTX 280 plus 2 HDDs (one at 10k rpm), 2 sets of 12" CCFL's along with a dozen fans with no issues for about a year. PC Power and Cooling wattage specs are with the PSU at 50°C. Well, they used to be when this one was purchased.
I have the 750 watt version of that psu, it should be fine (fantastic PSU really). Nearly 10 years old and flawless.
Usually when a psu fails, you see it on other things first, I.E. a dead dvd-rom, dead hard drive, usb sticks start failing for no reason... The motherboard has on board power regulation, so it's usually the last to go.
I'm assuming you have done the malware testing.
I recommend Malware Bytes, Super Anti-Spyware, TDSSKiller and Combo Fix.
Beware, the latter two can be like using a sledgehammer to squash an ant. TDSSKiller is a rootkit tool and Combo Fix does a rather deep scan, while I haven't seen either do damage (yet), the way they work can bring a system down. If you aren't sure, skip those.
First thing, I would do is check the system temps.
Once you know that's fine, before doing anything drive intensive, image the drive. On a failing drive, running a defrag can destroy it or at the very least the data. If I am extremely concerned for the drive, I copy out important documents and such before I even pull an image. Get the important stuff first. This way if the drive fails during imaging, you still have the most important things.
From this point you have a few options, from easy to difficult:
Try a different sata cable, I have seen them go bad and do cause extremely slow speeds.
Try a defrag using Defraggler, it will not only defrag, but also tell you if there is a S.M.A.R.T. error, though that only works a1/10th of the time.
Test the memory.
Last resort, if you have a spare drive, image onto it and put that in and see what happens.
If that all shows good, odds are it's the mobo. The sata system may be failing.