I don't know what KingofGnG posted, but judging from the posts of everybody else, using The Pirate Bay as a way to download "free" and "open source" games was clearly not what I was asking for, not even close... ("where to request a proper Offline Mode for the Steam client".)
Anyway, I made some tests this morning. My gaming and personal computer has a WiFi connection for the Internet using an USB device. So getting my PC without Internet completely is easy with just unplugging the WiFi device.
So, to simulate a situation where I don't have Internet at all without prior preparation, I unplugged the device and started the Steam client this way (no Offline Mode selected before), and found the error with the "No Internet connection". Selecting "Offline Mode" from this window started succesfully the client, with all the games I have installed, and could play a few of them without problems. Then, I closed the client properly.
Now, "going to the future" for 3 weeks just changing the system's clock (is there another way?), my anti-virus jumped telling me that I haven't updated my database, blah, blah... (LOL). Re-starting the client showed me the same message as before, and selecting "Offline Mode", I had no problems with the installed games, they were there and I could play a few others as well.
Same results going two months into the future.
Now, the only issue I found was that during the "Offline Mode" was active, I couldn't restore any previous backup I've made. I use an external hard drive to keep a backup of all my Steam games I have downloaded in the past (to not download them again), and when this mode is active, the client doesn't let you install any backup. Probably due that it needs to check online if you own the game and any update it may have.
Anyway, I couldn't reproduce the problem where others can't load the client after a while. In my case, if someday I don't have an Internet connection for a while, I guess I'll have to install previously any possible game I will need during that time, or else... (:P)
Post edited September 01, 2013 by Azrael360