> Do you have any idea how could he do that without changing my password ...
Of course -- he logged on as you. How could Skype (or your friends) distinguish him from you, if both he and you use the same username and password? In fact, for his purposes, not changing your password was to his benefit, because it helps him cover his tracks.
> ... my password was a combination of letters and numbers
If your password was robust, then I recommend that you scan your system for a keylogger. Also don't use the same password in more than one place.