Take a look at this thread:
Although it's about update to WP 3.7 the problem seems to be similar. Also from what you're saying I'm pretty sure this has nothing to do with WordPress itself as the error means that your system cannot establish connection with WP servers.
I guess there might be some kind of DNS isssue on your server, maybe also some kind of weird firewall setting or misconfigured hosts blacklist. Anyway you should just wait a few hours, a day maybe - if there'll still be the same problem you should definitly push your host (admin or support team) hard, because it's almost certainly their fault.
Good luck!