I've done a search already, and from what I can see the problems and solutions there don't seem to be quite like what mine is.
I've got WordPress set up on a Windows server on a corporate network, and although it broadly works, none of the RSS feed import plugins are managing to connect with the originating site and import RSS, and the internal WordPress dashboard functionality which needs to talk to the outside world (updates, theme & plugin browsing & installation, and the newsfeeds on the dashboard home page) also doesn't work - giving results along the lines of RSS Error: WP HTTP Error: connect() timed out!, RSS Error: WP HTTP Error: couldn't connect to host, and An Unexpected HTTP Error occured during the API request.
Akismet at least works (because They've been able to create a firewall rule so it can talk to the Akismet servers), but wordpress.com stats doesn't work.
I'm assuming it's a firewall issue rather than the http.php issue that my searches have thrown up, because it's a brand new version of WordPress rather than an old one, so if it is, what firewall rules do our firewall administrators need to configure to allow WordPress to properly talk to the outside world? Having to configure the firewall to allow the ip address of each individual RSS feed through isn't really practical, and installing WordPress on a Linux box rather than a Windows box isn't an option.