CPU fan cyles fast/slow - annoying noise

The computer is three years old but is fast and runs Win 7 ultimate. It just started making an annoying noise. It is definitely the fan on the mother board very close to the CPU (Intel Pentium 4 something). The cycle is faster than once a second and mimics a hard drive write. Touching the mother board clearly isolates the vibration and one can see the fan speed up and slow down. At first I thought something was overheating but it does this as soon as the computer turns on and continues indefinitely.

OK - "Replace the fan" That is a major nuisance and I am hoping that some really clever person has a neat solution; e.g. oil it or twist the board (scary) or something like that.

There are some old threads about noisy fans but those descriptions don't seem to fit my situation.

Thanks in advance. I have gotten some really clever advice on this forum.

:) Amazed by your speedy reply. It popped up on my screen just before midnight and I decided to sleep on it. Since I did several things, I can't be absolutely sure what the problem was.

I removed the fan from the mother board and turned on the computer for a few seconds. The fan continued to speed up and slow down so I don't think it was the mounting screws and certainly not an overheating problem. (?)

I had already cleaned this fan as part of a general refurbishing of the computer. However, while the fan was out I cleaned it with a Q-tip dipped in alcohol since some grimy dust remained. Then I oiled with light machine oil. Not sure that is a good idea but I was desperate.

Back to together and Voila - no noise. THANKS.

(I refurbish donated computers and give them to local non-profits. I am definitely an amateur but I have seen a lot of old computers. I have seen a lot of weird problems. About half I toss but the rest are greatly appreciated. This one with Win 7 Ultimate and a 3.2 GHz processor and 2 GB RAM is much too good to toss.)