Shoutbox

Are you sure you wrote the number correctly?
I can't find error #81000313 anywhere

Edit: I see in the title you put 81000314, so I'm going to go with that.

1st: Try opening your Internet Explorer browser and make sure that File > Work Offline is NOT selected. This will help.

2nd: Did you try using the troubleshooting tools available inside Live
Messenger,. Try using that and there is a repair button also and in 90% that solves the connection issue.

If neither of those work, you could try and do the steps indicated inthis website. but I recommend you wait. It'll be fixed soon on its own.