Mac Mini fan won't turn off (only while powered on)

Question

Unlike some stories i've read while crawling around the internet trying to solve MY problem, it's not that my fan won't shut off EVER. The fan shuts down when i put it in sleep mode or shut down the Mini. No problems there. But while the computer is in operation, the fan runs non-stop.
It wasn't always like this. In the 2.5 years i've had my Intel Mac Mini, it has more and more frequently employed the fan. As of the last couple months, the fan is now in continuous use, as long as the computer is in operation. In addition, all the programs take much longer to load, and i'm dealing with programs crashing (Firefox & Safari far more than anything), Bluetooth not functioning, and the front light on my Mini is out.
As for the fan, the Mini is getting plenty of breathing room...even more than it had before the problem. I also have 22GB left on my Mini's hard disk.
Are all these problems related? Am i really just working on my last thruster here? Is my dilitium crystal just about dead? Is a warp core breach imminent? I do not have AppleCare, and i don't know if the Apple Store would look at it for free if i brought it in. Any help (no matter how small) would be greatly appreciated.
MY STUFF:
Mac Mini - 1.66 Intel Core Duo, 2G 667 HHz DDR2 SDRAM
Iomega MiniMax 1TB external HD (for audio/video files)
Iomega Minimax 1TB external HD (for Time Machine)
OSX 10.5.6

Answer 1

When you start your mini from cold (after at least an hour powered down) does the fan spin up to full speed immediately, or does it start out normally and then speed up after a few minutes or so? Did you have the system open for any reason just before this behavior started?
If you had the system open, it might be something as simple as the fan control cable that is not connected. When disconnected, the fan will run at full speed all the time.
It the fan runs at full speed almost immediately from cold, then it would suggest one of two things: either the system is suffering from something like a loose heatsink, or there is an errant process running that is putting the system under heavy load. You can check that by opening Activity Monitor (in Applications>Utilities) at looking to see if the CPU load is consistently high. If it is, look for a process that is causing it.
If the fan runs quietly at first, and then speeds up, after a few minutes, then it does seem likely to be a heating issue. Aside from making sure the vents around the base and on the back are clear by using a good vacuum cleaner, it's possible there is enough debris inside to obstruct the airflow. If you've opened up the system previously for any reason, now might be a good time to do so again, for a quick inspection and clean out.
I would also perform an SMC reset if you have not already done so:
To reset the SMC on an Intel mini:
-From the Apple menu, choose Shut Down (or if the computer is not responding, hold the power button until it turns off).
-Unplug all cables from the computer, including the power cord and any display cables.
-Wait at least 15 seconds.
-Plug the power cord back in, making sure the power button is not being pressed at the time.
-Then reconnect your keyboard and mouse to the computer.
-Press the power button on the back to start up your computer.
And to ensure you are not suffering from a range of broad 'tuning' type issues, download a copy of YASU (http://jimmitchelldesign.com/projects/yasu/) and run all tasks. This clears cache files, resets logs files, updates prebinding, performs a permission repair and a few other tasks. After the reboot (which will be slower than usual) your system should run a little better.
... i don't know if the Apple Store would look at it for free if i brought it in....
You can make an appointment at the 'genius Bar' of your local Apple store - they will look at your system for free, and help with a diagnosis. What they generally wont do without charging for it is anything that involves opening the system up. However, it's worth paying them a visit for a bit of hands on work!