computerslayer1 on "Update checks, Feeds, and are inaccessible"

I just updated to 3.7.1 from the latest version of 3.6.

After upgrading, the dashboard feeds simply displayed the error "RSS Error: WP HTTP Error: couldn't connect to host".

Update checks produced errors in log files:

[05-Nov-2013 17:38:53 UTC] PHP Warning:  An unexpected error occurred. Something may be wrong with WordPress.org or this server’s configuration. If you continue to have problems, please try the <a href="http://wordpress.org/support/">support forums</a>. (WordPress could not establish a secure connection to WordPress.org. Please contact your server administrator.) in /home/.../public_html/wp-includes/update.php on line 112
[05-Nov-2013 17:39:05 UTC] PHP Warning:  An unexpected error occurred. Something may be wrong with WordPress.org or this server’s configuration. If you continue to have problems, please try the <a href="http://wordpress.org/support/">support forums</a>. (WordPress could not establish a secure connection to WordPress.org. Please contact your server administrator.) in /home/.../public_html/wp-includes/update.php on line 259
[05-Nov-2013 17:39:17 UTC] PHP Warning:  An unexpected error occurred. Something may be wrong with WordPress.org or this server’s configuration. If you continue to have problems, please try the <a href="http://wordpress.org/support/">support forums</a>. (WordPress could not establish a secure connection to WordPress.org. Please contact your server administrator.) in /home/.../public_html/wp-includes/update.php on line 399

If I go to the "install plugins" plugins page, these error messages are displayed:

Warning: An unexpected error occurred. Something may be wrong with WordPress.org or this server’s configuration. If you continue to have problems, please try the support forums. (WordPress could not establish a secure connection to WordPress.org. Please contact your server administrator.) in /home/.../public_html/wp-admin/includes/plugin-install.php on line 77

An unexpected error occurred. Something may be wrong with WordPress.org or this server’s configuration. If you continue to have problems, please try the support forums.

Basically, it looks like this installation of wordpress can't access any sources of data hosted outside of wordpress.

Any ideas?