Thanks for your reply.
I have a Logitech Elite, I never had any problem with it and I'm pretty sure the problem has nothing to do with it.
I didn't run any compatibility mode and I tried a lot of different settings from the highest to the lowest and nothing changed beside the framerate result of benchmark but it was good each time.
I can't post the benchmark anymore since I have a new problem:
I uninstalled the game and tried to reinstall it, hoping it would solve the problem, but now, I can't install it anymore, it gives me a error message (Error Code: -5001 : 0xffffec75) everytime I try to install it.
I tried to remove anything related to GTA IV (RGSC, C++ thingy...) then reinstall everything but nothing changed. I copied the files on my hard drive to try to install from there, didn't work either, I'm totally lost and I'm starting to think of returning the game and use my money to buy a real working game.