Good ideas.
Just wanted to add step 3 can be a solution it your ISP or domain DNS server is not working but lately the Google Public DNS servers are slow, over twice as much time to resolve a name then my ISPs server. I would suggest if you think that you ISP DNS is an issue you use 8.8.4.4 as a secondary and your router IP/Default Gateway as primary.
ipconfig/flushdns is good to clear out cached dns data that is wrong/corrupt
Just a note for anyone having issues Limited Connection is a generic error and if you continue to have an issue start a new thread and add the steps you have tried to resolve the issue so that you can get help