I was trying to figure out why Steam kept refusing my login attempts. I checked that I was using the right password and username. I checked that caps lock was not on. And finally I did a quick search and found this very useful site that shows that at the time of this posting, Steam is down. http://issteamdown.com/ So if you, like myself are wondering why you cannot use Steam in any way, you can check that URL to see if it is specific to you or if Steam is not working at the moment.
There's a low spike in Steam's on-line users data every day, my bet is that you tried to log-in during that time
Actually I have been trying to login for about two hours. It still refuses the attempt. I checked my firewall and even disabled it and anything else that could get in the way of it. But it is just Steam being less usable than normal. I presume this is some maintenance that will be over and done some time tonight or tomorrow. But Steam does not have this listed on the Support or maintenance sides of the site, and the site itself is working fine. (It even lets me login to the same account that I cannot use at the moment with the Steam client.)