Half serious answer: have you considered Linux with a Windows Emulator?
Serious answer: depends if you got this issue because your machine has been off the internet for a long period. The last one I had to fix was caused by this. From what I can see the cached authentication credentials for the Microsoft Account are just like a domain login: they expire after a period of time and you cannot get back in until you connect the device to the domain network. In this case the "domain" network is Microsoft.com via the internet.
If your device is always connected to the internet, which several of the posters to this thread seem to be, it is harder to understand and to fix. I found by stopping the device from sleeping and leaving it hardwired to the router via ethernet after a couple of hours I could get in with the PIN again. What initially stopped it from doing this is that if you left it alone unobserved it went to sleep very quickly shutting down the internet connection. I had it on my desk at work and kept moving the mouse pointer to keep it awake at intervals. I suspect if you can get it connected to WiFi and keep it awake it might do the same thing.
hope that help you.