Yes, Just as long as the Xbox 360 slim you have is the 250gb version or the 4gb version with an internal hard drive inside it. It does not work without an internal hard drive. It will not work with a usb memory stick or external hard drive.
I believe that the 4 gb xbox 360 you are talking about is the new slim. There is no way to use your old hard drive with the new slim xbox. You will need to buy a transfer cable to move your saved games to the 4gb hard drive.