If the Steam Network is down or too busy you may not be able to connect to a Game Server at this time!
You can always look at the Steam Status Page and see if there is something is going on. If the last update for that page is more then 20 or 30 minutes behind, that is a good indicator of a problem.
Please also check to see if there are other players having the same problem on the Steampowered Forums.
If the Network is down, you will just need to be patient and wait until the problem gets cleared.
If everything else seems to be ok and no one else is reporting this problem then you should go to the Settings menu in Steam and choose Login as a different user, then log back into the account you were having problems with.
Normally, if this is a problem on your client it will prompt you to renew your Ticket.
If this seems to happen with one Server but not others, then that Server might be having network problems. Especially after an outage of the Steam network, it may take a while for Servers to clear their status and let you connect.
You do not need to re-install Steam if you have this problem.