We use MAK keys and have never had a KMS server. KMS is optional. If you push out Windows to a ton of machines and don't want to have to go around and activate each one by hand, you can open up KMS and activate all of them, or have it done automatically. You can even switch keys from the KMS server to numerous machines. Very handy in a large environment.
Alex, try this command:
That will display your current licensing status.
I would try, as Kelly suggested, re-entering the product key. That has fixed most issues for me. I do know that some updates have broken the activation for some machines here, but not all. Very weird. Re-entering the key worked every time so far.