Actually, JustinD is incorrect. Microsoft is very specific about how OEM keys work. Specifically, they are tied to a specific hardware and activated as such. During the activation process, they tend to take an inventory of components and recognize the key based off that (the motherboard is included in those).
So what that typically means is that the OEM key from the first laptop is tied to that Laptop. However, you may be able to use the key that probably came with the new one. Otherwise, you could call MS and see if they will work with you - but it is highly unlikely.
- I would try to activate with the key that likely came with your new computer before trying to deal with MS. They rarely bend the rules on the OEM installs.
Per Microsoft's FAQ & Licensing page
Q. My customer bought a new PC and wants to move the OEM software from the old PC to the new one. Can't users do whatever they want with their software?
A. No, the OEM software is licensed with the computer system on which it was originally installed and is tied to that original machine. OEM licenses are single-use licenses that cannot be installed on more than one computer system, even if the original machine is no longer in use. The End User Software License Terms, which the end user must accept before using the software, state that the license may not be shared, transferred to, or used concurrently on different computers. System builders must provide end-user support for the Windows license on computers they build, but cannot support licenses on computers they didn’t build. This is a fundamental reason why OEM System Builder licenses can't be transferred.