The Dimension 3000 uses a BTX motherboard (although the power supply is standard ATX). There is a system fan, but because it is a BTX chassis the fan is set up to pull air through the heatsink assembly and out of the back of the system.
http://support.dell.com/support/edocs/systems/dim3000/en/SM/parts.htm#wp1055121 is the section of the service manual dealing with removing the heatsink and CPU.
http://support.dell.com/support/edocs/systems/dim3000/en/SM/parts.htm#wp1055464 is the next section, which deals with the system fan. The power connector for the system fan is between the memory slots and the CPU socket, towards the left (back) part of the board.
When removing the it, I highly recommend gently but firmly twisting the heatsink assembly back and forth to break it lose from the CPU. If you don't do this you run the risk of pulling the CPU out of the socket while it is still "locked", which has the chance to pull one or more pins out of the CPU (which is not a fixable problem).
As others have stated, you will need to clean the old thermal grease off the heatsink and CPU, and then apply new if you remove the heatsink from the CPU. This is so you have no gaps between the CPU and the heatsink for heat to get trapped in.
If you have any questions about the Dell system I will be happy to answer them.
[edit]
Apparently, we were both typing replies at the same time.
If the only problem is corrupt Windows files (probably due to the system shutting down unexpectedly) then you should be able to do a repair using the Windows CD. If you want to make sure your data is safe first, then I would recommend either pulling your hard drive and mounting it in a working computer as a secondary drive or getting a second hard drive and installing Windows on it with your original drive as a second hard drive. With your hard drive as a secondary in a working computer, you should be able to access the files and back up your information.
You might be able to fix the problem by booting from the XP CD and using the recovery console to run "chkdsk /f /r /p" to have it check windows files for problems and repair them). If the only problem is a few corrupted files your data should be safe, but unfortunately there is no way to garuntee it, so you may want to back up your data first anyway.
Larry
Dell Customer Advocate