Basically, Microsoft says there are six steps that need to be tried when the Surface is suffering from limited or no Internet connectivity.
Solution 1: Install the latest updates for Surface
Solution 2: Check your date and time settings
Solution 3: Restart Wi-Fi on Surface
Solution 4: Restart network hardware and restart Surface
Solution 5: Run troubleshooters
Solution 6: Manually reinstall wireless driver
https://www.microsoft.com/surface/en-ca/support/networking-and-connectivity/cant-connect-to-a-wireless-network?os=windows-10#other