This fan stopped working, and the computer would shut down unexpectedly. Although I really should get another computer, I would first want to ensure I have a full backup and there were things I wanted to get done NOW.
The fan is right there, under the back cover. One screw and you are there. To replace it, you pretty much take the computer completely apart, starting with the keyboard and ending with the mother board.
A box fan positioned underneath to blow air over the heat sink. Worked great but it was like sitting in front of a wind tunnel.
The need for a more permanent solution was based mainly on the fact that it takes me forever to make a purchasing decision. I found a computer fan in a box doing nothing worthwhile. A smaller one would have been better, but this is what I had. I had plans on making a mat to direct the airflow to the heat sink out of cardboard. Then, while rummaging around in the closet, I found the original box for this computer.
Cut a few holes.
Place a fan on the box.
Place the 'puter on the box.
Wire it up, and you are done.
As shown above, to replace the fan, you pretty much take the computer completely apart, starting with the keyboard and ending with the mother board. Flea-Bay has these fans as take offs for under $5.
U-Tube has videos of "Technicians" taking the computers apart, and it is not pretty. I hate U-Tube how-to videos. You spend 15 minutes watching a video of someone who has never done the job show how he did it, and it turns out to be wrong. What a waste of time.
The stars show where the three screws are. One is easy, another requires minor removal of plastic, but the third, well that requires a leap of faith that there is nothing under the plastic to cause a problem.
This computer cost me $300 three years ago, it has served me well, has spent a lot of time bouncing around in the trunk of my motorcycles, and is set up just the way I want. Although I will replace it with a new unit, it is still worth fixing. So . . . .
"New" fan for $3.93 delivered through E-Bay. This one had the same part number and was exactly the same as what was there. I found a lot of fans that were similar, but this is the only exact one I found. It was the cheapest one as well.
The other side.
Yes, it was used, but who cares. New ones were over $30 delivered. 
I used a small knife to make clearance for this screw. It turns out the screw was very short and all I needed was clearance for the small screwdriver.
Lining up the new fan on top of the old one to see where the third hole needs to be drilled.
This hole was drilled carefuly as I did not know what else was in the area.
It turns out the memory card was in the way. 
The memory card comes out in seconds.
But the fan would still not come out. I had to make room for the housing that held the third screw.
A little work with the dremel and I was done.
There were a number of components around the screw. Had I dremeled just a little bit more there might have been trouble.
The old Thermal Paste, partially removed from the processor.
The processor nice and clean, waiting for new Thermal Paste.
A small tube of thermal conductive paste. Use it sparingly. It actually cost more than the fan. 
You want to be very careful that you put on just enough paste and not too much, and make sure it is even. THIS was not my final try, this is too messy. Thermal paste is there to transfer the heat from the processor to the heat sink that is part of the fan. 
"New" fan installed. The heat sink is to the right of the #3. The processor is directly under that. All the air from the fan blows through that to cool everything down. A LOT of heat comes out the side of the computer when it is on. My new computer has no fan, it uses the body of the computer to eliminate the heat. Not as good at keeping the processor cool, but simpler and no fan noise. 
The fan is spinning, and all is right in the world again.
