Thank you so much every one who helped me on my 5.1 > 5.2 upgrade. It has finished nicely and down time was only one minute if it was not less.
I finally found which inc file I modified. It was menu.inc required by menu_per_role module. When I updated my local server, it was obvious since all the menus those which shouldn't be showing got visible :-)
So, I ended up this way. Note that, I don't know what is the correct term in English about this, I do have subdirectory setup as the root of my site. I initially did this in preparation for upgrade, and I think it paid off.
I first upgraded on my local server then run test drive I duplicated the directory then replaced the settings.php with the live one Zipped it up Upload Unzip it on the server Take the live site off line Rename the 5.1 directory to 'old' Then rename the 5.2 to live one
Just for checking, I accessed right after renaming the live directory, and got a server error instead of the Maintenance message. As soon as I renamed 5.2 directory to live one, all came back right away.
All in all, I was pretty happy how it went.