Is it possible to log your Steam account into two computers at once?

As several people have mentioned, it is now possible to be logged in on multiple computers at once. Only one computer can be playing a game at a time though. If you start a game while another computer is already in one, you will be notified and told that it will close the other game if you start.

As of the recent Steam Streaming update, yes, it is now possible to log in to one account on multiple computers at once. You can just log in as normal; it no longer logs you out on other computers.

I'm not sure if this has been confirmed to work on multiple networks.

As already said is not possible to be connected to Steam with the same account in more than 1 computer at time.

But maybe this QA can solve your problem: How to continue downloading a game in Steam while playing?