I have the same error message on my Windows 8.1 RT Surface when trying to connect to a Microsoft Account: "Sorry, we couldn't connect to Microsoft services right now. If this problem persists, search for 'network problems" on the Start screen."
I changed the Microsoft Account sign-in Assistant service to "automatic" (it was in manual mode) but this did nothing.
The machine is pretty useless if you can't access the Store to download a few essential apps or sync your OneDrive account.
Please fix this ASAP.