The error code simply means ERROR_INTERNET_CANNOT_CONNECT, so you'll have to troubleshoot your Internet connection.
Start by resetting your modem (switch it off, wait five minutes, then switch it on again). Try synchronizing your Hotmail account again.
If that doesn't help, check your firewall to make sure that ports 25, 80, 110, 119, 143, 443, 465, 587, 993 and 995 are open for Windows Live Mail to use, or trust the program to use any port it wants to.
Make sure any third-party anti-virus software isn't scanning email. You don't need it to, and it can cause problems.
A long shot: in Control Panel, find and open Internet Options. On the Advanced tab, make sure that SSL 2.0 and 3.0 are not enabled, and that TLS 1.0, 1.1 and 1.2 are enabled under Security:
Also in the Internet Options dialogue, there should for most users be no entries at all on the Connections tab. Click LAN settings: that page should normally be empty, too.
If you make any changes, please try send/receive in Windows Live Mail after each one so we know which change - if any - solved the problem.