delete everything in the steam directory except for steam.exe and the steamapps folder? Then run Steam.exe and it should download everything, see if that works?
Disable the firewall completely?
https://support.steampowered.com/ Hit the contact support, create an account (Its not the same as your steam account), and make a ticket?
Disable the firewall completely?
https://support.steampowered.com/ Hit the contact support, create an account (Its not the same as your steam account), and make a ticket?