Thanks to all who contributed to this thread.
The problem is now almost solved.
The problem was that after installing iwlwifi, I could not take advantage of rebooting
because I was using a live DVD.
Apparently, after installing iwlwifi, I needed to reboot. But rebooting with a live DVD would not make much sense.
So, I decided to install debian 7.
After installing iwlwifi on the installed system, I faced the same problems. But rebooting fixed the issue.
Now wireless is working.
Does anyone have any idea as to how the solution could extend to a live environment?
Mind you, in a live environment, logging out and logging in did not work.