So here's the thing, I own a Compaq laptop and my screen broke. So instead of buying a new screen, I'm getting a Dell laptop from a friend because his hard drive went out and he doesn't want it anymore. So I want to swap the hard drive from my compaq with the one in the dell. Will it work?

Yes, but you'll need to reinstall the Operating System due to hardware changes.

As mentioned, would need to get drivers for the machine you are installing it to and need to make sure the drives are same type. Probably both are IDE hard drives but need to make sure they are. Make sure the drive has the same connection as one replacing as there are the SATA drives and IDE drives. If both same type drives, should not be an issue other than drivers which you should be able to get from dell's website with the model #