Well, I got it up and running.
I changed my PHP version from 5.5 to 5.4, and everything seems fine now.
BuddyPress is not compatible with PHP 5.5 or what?..
@mercime @henrywright @djpaul
Thanks folks for the suggestions, but it doesn’t seem to be my case…
I did all that with a freshly installed WordPress, with NO other active plugins and with the Twenty Fourteen theme (it was active by default).
I have just tried once more and switched to another standard theme (Twenty Thirteen) before the BuddyPress activation, but I got the exactly same result…
Is it possible that the problem is connected to my hosting configuration?