XPS 8700 fan speed

My computer has had occasional problems where it will shut down without warning, similar to when there's a power blackout. The computer won't turn on by pressing the power button immediately afterwards, but after allowing some time it will turn on and return to entirely normal running, no error messages or the like at any point. At every point it's happened it's been while/shortly after running a heavy load; it's never happened while idle.

At the time this happens the vents on the back are extremely hot to the touch, so I installed HWMonitor to check the temperatures, and watched it while running games that have stressed it. The CPU(i7-4790 that came with the system)  and GPU(I upgraded when I bought to a GTX 660Ti) sensors never rose much above ~80c, but I did notice an oddity in the program in that my cpu and gpu fans seem to always run at ~750rpm, regardless of whether it was idle or under heavy load.

I tried running the system briefly with the case open (cleaned and dusted the inside too) and an exterior fan blowing as well, the power supply was still extremely hot to the touch within ~30 minutes of gaming while the rest of the inside of the case didn't feel hot

I'm a bit stuck on how and what to test to find the problem; is the power supply not enough to handle the components? Is the power supply overheating? If so, what can cause that and is there a way to test it, and how can I tell? Is the fan speed a sign and/or symptom of the problem? Is there a way I can try to 'force' the fans to spin faster to see if they're being physically obstructed or just not being instructed to spin faster when under a load? Whats the best way to go about trying to diagnose the situation?