had this same problem. here's what the steam guys told me to do and it (sorta) worked. Now I can at least randomly connect, but even if i can't connect I can play games in offline mode.
Please try completely removing Steam and re-installing. You may want to print out these instructions for quick reference.
1. Write down your Steam Account name and password - you will need them to log back into Steam once you have reinstalled
2. Logout of Steam
3. Exit Steam
4. If you currently have any Steam games installed that you would like to keep, please copy the Steamapps folder from C:\Program Files\Steam to your desktop or another directory.
5. Delete the Steam folder in the default location C:\Program Files\Steam
6. Hit windows key + r ( run at the start menu ) and type regedit
7. Delete HKEY_CURRENT_USER\Software\Valve and HKEY_LOCAL_MACHINE\SOFTWARE\Valve (or HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Valve on 64-bit Windows)
8. Download and install the Windows Installer CleanUp Utility from the following link: http://www.majorgeeks.com/Windows_Installer_CleanUp_Utility_d4459.html
9. Run Windows Install Clean Up from the Start menu.
10. Select Steam from the list. The list is only partially in alphabetical order, so be sure to check carefully.
11. Select Remove.
12. Select OK.
13. Reboot your computer.
14. Download and install a fresh copy of the Steam installer from http://store.steampowered.com/about/
15. Run the installer and re-test the Steam client.