Maybe you can solve your problem with steam with a complete fresh install of Steam.Go to
http://www.revouninstaller.com/revo_..._download.html Download Revo-unsinstaller.Just choose the Free version.Use Revo-uninstaller to uninstall Steam.If it is done, restart your pc.
Go to
http://store.steampowered.com/ and install Steam again.
I install things like this with UAC turned off and all with administrator rights
Maybe you can check your settings of your firewall, maybe you are just blocking Steam.