If it's a OEM license then no you can't move it. OEM license are the ones that come with the computer from the factory. You can also buy them online for a cheaper price than the retail version. However, the one restriction with OEM is, it can only be install on one PC ever. It also has limit upgrading room. For example, I believe replacing the motherboard will cause the license to be invalid for the upgraded PC.
If it's a retail license then yes. Retail license can be moved to another system as long it's only installed on one computer that is functioning. You may have to call MS support to activate it, though.