"Limited or no connectivity" is not and has never been a bug .... rather just a bad choice of words by Microsoft.
It happens when an IP interface is configured to get its IP addr automatically (dynamically) and it never recieves one (e.g. no DHCP server around). That covers the 'no' part.
When the interface doesnt get an IP addr assigned, it falls back to a private address randomly selected from the range 169.254.0.0 as per rfc3330. Thats the 'limited' part.
What the message should read is "Automatically assigned IP address was not recieved, using private IP address" but I suppose MS thought this would be confusing to newbies.
This message can be rectified by ...
- making sure there is a DHCP server around to provide an IP
- changing the interface to use a statically configured IP
- disabling (unticking) TCPIP completely off the interface
The reason why this message is usually associated with broadband connections, is that ppl mistakenly assume PPPoE requires IP to operate. While PPPoE carries IP as a payload, it uses direct Ethernet MAC addr to MAC addr communication to forward packets (basically bridging), hence its name PPPoE not PPPoIP.
Since broadband modems e.g. ADSL, iBurst, myWireless etc. (not routers) only talk PPPoE and not IP, one can disable (untick) TCPIP from the Ethernet interface directly connected to the modem, thereby eliminating the "Limited or no connectivity" message without affecting the broadband connection that passes through it.
The only exception to this is if the same interface is used for some other IP communication as well the PPPoE. Then setting the required IP addr statically should be done (since if there was a DHCP server, you wouldnt get the message in the first place).
EDIT NOTE: I've seen this question asked so many times in this and other forums, I thought I'd expand it to the full explanation.