I have a quick question to ask. Ok I have a Gateway PC and old Dell Dimension PC. My hardrive for my Gateway isnt working. Can I take out the hardrive out of my dell and use it for my gateway?

While the hard drive will work, The operating system will not.
You would have to reinstall your operating system. This will cause you to loose all of your data so back up every thing first.
The reason for this is when you install windows it creates a number based on the machines hardware, and the operating system itself.
This unique number identifies the computer to the operating system so that you can not copy some one Else's hard drive and steal the operating system.

At the least you will need to do a repair install of Windows, You will need the Restore CD for the Dell computer or a Windows CD with a CD key. You can download system drivers from Dell if you have to do a complete install. Here is a tutorial on how to do a repair install.

Edit: In the off chance you have to re-activate windows make sure you know what your Dell licensing key is for windows.