Ok, I unplugged all the HDDs, and the the SATA/IDE cables from the motherboard itself.
Then I turned on the PC, and let it load up until it reached black screen that displayed this message "Reboot and select proper boot device or insert boot media in selected boot device".
Then I just left the PC as is, with the message still displayed there, and proceeded to inspect the fans.
As far as I could see, all the fans were spinning as usual, there were no "dead fans".
The CPU fan looked normal, as far as I could tell.
The PSU fan also looked normal, as far as I could tell. Both the PSU fans, the one with the golden grill, and the one blowing air out, were spinning as they should, nothing abnormal. The fan was blowing out warm air, I could feel it when I put my hand near it.
To shut down, I just pressed the power button on the CPU.
As it shut down, the fans stopped spinning, nothing abnormal as fas as I could tell.
I didn't know what to look out for, so I just looked at which fan stopped spinning first.
When I pressed the power button, the PSU fan was the first to stop spinning completely, followed very closely by the CPU fan. This may or may not be of importance, I don't know.
Other than that, that's as much as I can tell you from my observation. As far as speed is concern, to me all the fans were spinning very fast, there were no abnormally slow-spinning fans. How fast exactly, that I couldn't tell.
The PC ran for about 2 hours non-stop, without auto shutting-down.
I forgot to mention that I did, at one time, did a test and left the PC on, with DVD drives, floppy drives, HDDs, all still attached. Once it loaded past the welcome screen, I just let it be and did nothing. I left it on for 3 hours straight, followed by a voluntary shutdown. I guess it stays on if I do absolutely nothing, but once I started doing something like web browsing, or checking some files, thats the time when its most likely to happen.