This is how I fixed a troublesome heatsink fan clip on a computer I was given recently.

I used an eraser to adjust proper tension in these clips!
I picked up this computer told that is is probably working. The specs
were Celeron 2.4 in a small desktop case with AGP micro-ATX motherboard.
This is more than enough speed for most things I do, so I decided to
spend a bit of time seeing if it would run.
At first, it
wouldn’t boot until I took out the CMOS battery. That got it to POST,
but then had some more intermittent errors and finally couldn’t boot
again. I have never like the squeezey-tension heatsink fan clips which
Intel started using I think around PIII or early P4 times. They always
feel like they are going to break when you add the tension. If the CPU
was hot from not enough contact, I wanted to see if I could get better
surface contact between the CPU and heatsink. I took it apart and
cleaned the old budget thermal paste from both surfaces. Sometime after
that, I found that the system would only boot when I relaxed the tension
out of the heatsink fan clip. The CPU temp as monitored in the BIOS was
what I would call normal. If I completely removed the heatisnk, it
would quickly rocket to over 90 degrees centigrade.
I just ran
the machine like this for abuot a month, as I had it in a desktop case,
so the laws of nature would hold the heatsink to the CPU with enough
force to make contact. Today, though, I moved the internals of the
computer to a nice big tower case at work. To prevent the relaxes clips
of the heatsink/fan assembly from letting the heatsink lose contact with
the CPU, I found a nice DIY method for adding just enough tension to
this type of heatsink fan clip to make contact with the CPU but not
strain the motherboard or cause whatever problems I was having from
over-tensioned clips.
My magic fix-it material today was a
rubber eraser cut into perfectly sized blocks!! I pulled the tension
levers uo to 90 degree angles, first on one side, then the other. As I
lifted it up and it created space between parts, I squeezed in a
slightly overisized piece of rubber eraser and then let the tension
lever back down, allowing the eraser to hold the perfect amount of
tension between the heatsink fan clip and the CPU.
With both
sides done, this machine now boots and runs stable in an upright tower
case. I recommed trying this technique for machines with the same
troublesome CPU heatsink fan mount which is failing to boot.