Windows transfer onto new system?

I have a laptop with windows on it, and I might be getting a system this christmas. However to save money I need to go with linux. However...

If I copy my laptop hard drive to this desktop hard drive will that work without having to buy a windows license? What if I restore it?

I have tried that and no it doesn't work if I recall it was because of windows genuine protection.

Microsoft is a bit picky, honestly. If you bought a separate copy of Windows (say when you've built a desktop), they'll let you reuse the key on a new system. However, for laptops with windows pre-installed , they don't allow you to reuse the copy of Windows (supposedly). That being said, I have a copy of Windows 7 in a VM that I reused from my first laptop that's now a router. I left it off the windows partition for a few months, then it gave me no problems activating it in a VM.