Well then, it literally just shut down on me while I was typing this reply, and the mystery is officially solved: the CPU fan control (and other stuff as well) go completely bonkers after sleep mode, and the CPU overheats. The last report was for 87.4°C and the mobo shut itself down (or did the CPU? one of them) to prevent damage; if the CPU is still in critical temp after shutting down, the PC will refuse to boot up afterwards, that's why no POST occurs and that's why I had to turn it on many times and power cycling didn't do anything - however I've changed the temp warning mode, now it gives a beep at 70°C, so I can at the very least enter the BIOS to check the temps while the now rebooted fan dissipates the heat properly.
But yes, the PWM just doesn't seem to work correctly, either by issue of the circuit or the BIOS. The control curve and speed change appear to be working, i.e. it does not get stuck on a certain speed all the time, instead it goes up and down as the temp increase, except of course it's skewed down to half and therefore makes the PWM go 100% almost all the time due to high temps. However it's not impossible that it could shut the fan down altogether at times, as I wasn't fast enough to pay attention to read the reported RPM values once it shut down, yet the last value was 2647 RPM (which to the sensors means "off" apparently, I can verify this is true because the free system fan slots both report 2647 RPM for min, max and current value all the time and other people also confirmed as well).
Also that link you posted is for the revision 1.0, I have the rev. 4.0 (
GIGABYTE - Motherboard - Socket AM3+ - GA-990FXA-UD3 (rev. 4.0)) that only goes up to version F3 (2015/05/28). F4a was reported by some users as a beta they had received by contacting Gigabyte, but it's not out to the public, most likely F4 will be out some time soon. I can do a dual BIOS indeed if anything goes wrong, so I'll definitely look into setting that up to be safe. Of course, other solutions might include stop using the sleep mode altogether or changing mobo, or hacking the fan control in some cute way, though I'd rather not have to choose either of them. Hopefully they'll respond with something useful for me, but yeah I'll definitely use any beta BIOS very carefully
