Humm, I dunno how likely a PSU is to burst into flames

, but I'd be worried if the fan starts messing up. It's normal for recent PSUs to change their fan speed depending on how heavily they're loaded, but from your descriptions is sounds more like the fan (or perhaps the PSU itself?) is starting to malfunction. If the PSU is malfunctioning, it might be delivering unstable voltages to your motherboard, check the "hardware monitor" in your BIOS and see if it looks relatively stable (even my expensive antec PSU doesn't hit the right voltages 100%, and it also fluctuates a bit... I think it's around 0.1-0.2 volts off).
Single beep from BIOS stage is normal, to indicate that it actually works and your CPU isn't fried

Is the "gibberish on screen" just a lot of techno-jumbo text, or does it look like screen corruption? Any error/warning messages? CMOS corruption can happen if your CMOS battery needs replacement and you haven't had the wall socket the box is connected to powered on. It's not
necessarily a problem (though if it keeps happening, you should get the battery changed), and it might be a good idea to review the BIOS settings and see if things are a-okay.
When the machine actually hangs, is that (almost) always when windows is about done loading? Might not be a heat problem since your CPU fan keeps working, but it might be a good idea checking the heatsink to see whether it's clogged up with dust. Could also be voltage problem as mentioned previously.
Could be bad RAM, might be an idea to run
memtest86 on it for a while, after checking other things. Might also want to check graphics card fan/heatsink.
There's so many things that can go wrong with computers, *sigh*.