MrEvilness found the solution, as published in Steam's forums.
"if you did not gather i forgot to mention i switched the bios graphics setting from fixed to dynamic to get the game to boot >.< sorry for the confusion"
Our problem wasn't related to disk integrity nor registry. It's about the switchable graphics some laptops have. As usual, some games won't work unless from the BIOS the 'fixed' option is set (it allows only the 3d GPU to work, unpowering the intel gpu or whatever low performance/power consumption one has).
In this case, it's all the other way round, as MrEvilness states, it needs to be set as 'dynamic'. Odd.
---------- Post added at 21:41 ---------- Previous post was at 21:24 ----------
However, game is unplayable.
It's far away from running smoothly (even in low graph settings). Mouse is crazy, screen is glitching and fps are ridiculous. I repeat, unplayable.
And for instance I've played Skyrim with good settings and it worked smoothly, so it's not my computer the faulty here...
And when quitting game, a nice gift, I like purple, but not in this case: http://tinyurl.com/bn6gvb3