No, you cannot use that key on anything other than the laptop. You have an OEM version, and as stated by the EULA, it is tied to the original computer and cannot be moved to any other computer. That's why OEM is much cheaper than retail - retail can be uninstalled and moved to any computer, any number of times.
You know, you don't have to wipe the drive to install Linux. You can create another partition and install Linux on it, or you can buy another drive (very cheap nowadays) and swap back and forth to your heart's content.
If you want to install Windows 7 on your desktop, you'll have to buy a new copy.