Hey guys!
It finally worked.
I notices someone stated that one of the active plugins produces unexpected output, causing a “headers already sent” warning and consequently preventing WordPress from setting the test cookie.
But I received no message , only “Cookies are blocked…”
Trying to find a plugin (none of other measures worked), that causes such malfunctioning, I found that Justified Image Grid causes that.
Now login works as it should.
Will have to fix that plugin now =)