(Assuming your GF is using windows)
Right-click on 'My Computer' and go to 'Properties'. Under the 'General' tab, under 'Computer:', is your CPU.
Start>Run; 'dxdiag'. Next to 'Processor:' is your CPU.
[Instructions may vary slightly on Vista/Win7]
Now, if you can't boot into windows then you'll have to take off the case side like they said and remove the heatsink to read what is on top of the CPU itself. (You can also look in there to try and find out what motherboard she is using, that should give you enough info [for CPU socket] to get a new heatsink)
OR if it is a manufactured computer (IE: Dell, HP...) you can look up the computer itself to find out what CPU is in there. *shrug
Easy as 1, 2, 3.
1. Find out what CPU it is. 2. Look up the CPU to find out what socket it is. 3. Look up that socket to find a heatsink.
PS: The socket you we are finding is not for the fan, but for the CPU. Usually they generalize different heatsinks to different sockets, so if you know the socket you should be able to find a heatsink for it.