I experienced an odd problem on a Surface Pro (first edition). This happened shortly after upgrading to Windows 8.1 Update though not immediately after.
Symptom: I could connect to wifi but although I had five bars of signal strength, according to the notification area icon, I had no connection; and ipconfig reported “Media disconnected” for the wifi adapter. Tried a different wifi point, same problem. Rebooted (of course), same problem.
My next thought was another old favourite: reset tcp/ip with netsh int ip reset. Restarted, no change.
The fix I found was to go into device manager (which was not reporting any issues) and to remove the Marvell wireless network controller. Scan for hardware changes to reinstate same, and I was up and running.
The incident reminds me of how fragile Windows seems to be at times. One of the reasons I like Windows RT (the ARM version) is that its locked-down operating system should be more resilient though it is not immune (you can still scramble the registry if you feel so inclined).
Update: I may not yet be in the clear. Later in the day, wifi failed again, and this time the Marvell adapter showed in device manager with a fault icon. Enabling and disabling the device restored connectivity. A driver issue with the latest Windows update? Or failing hardware?