you can either call them or go through chat support and they will attempt to fix it, or issue a new key.
I had someone bring me a laptop with windows 8 on it. the motherboard got fried due to loose screws rattling around inside from a broken hinge.
ordered a replacement motherboard off ebay and installed it to the chassis (after repairing the hinge)
. key went invalid as expected (since windows 8, it now authenticates on the hardware not an actual physical key)...opened up MS chat support....explained the situation (that the motherboard died and I installed a replacement and windows would no longer authenticate the key)...they tried to fix the existing key, but for whatever reason it wouldn't take... so they ended up issuing a new key for the computer. not a problem. easy peasy. they did all the work remotely.
even if i transfer a win 7 key from one machine to another machine (which legally you can absolutely do) and it fails the online verification, just call the 800 number (free call) it gives you and follow the steps in the automated system type in the installation ID numbers... it asks if i've used it on another computer before, you say yes, one other computer (or however many times you have transferred it). then it gives you another number you punch in to authenticate windows. 10 minutes tops. 24 hours a day 365 days a year. Don't even have to talk to a person.
For clarity on my earlier point. There is a difference between transferring a windows key versus an OEM windows key. OEM keys are technically not transferable.