I finally upgraded one of my laptops to Windows 8.1 and my first immediate problem was the wifi adapter was showing "limited" or "No Internet Access". I know my home wireless is functional cause it works on other devices so I go through the motions of solving it.
1. Troubleshoot Problems with the connection - works only temporally
2. Reset wireless adapter - didn't work
3. Update drivers - no dice
This blog summarizes the 'workaround' from around the forums and other blogs I've seen. http://everythingsurface.org/4-ways-to-solve-your-windows-8-1-surface-pro-wi-fi-issues However my issue wasn't solved after trying them out. I know my wireless settings on my router to accept only Wireless-N connections at 2.4Ghz (don't ask why), but I also noticed in Device Manager for the wireless adapter that it is set to 'Auto' for 802.11n Channel Width for band 2.4. I changed it to 'Auto', restarted and the problem went away. Hopefully this adds to the workarounds for whoever is having problems with wireless connectivity on Windows 8.1