I do not have a straight answer to this, but I don't believe there is one anyway. Islam is neither monolithic nor static. There have been different, evolving strands of Islam, both Shia, Sunni, or otherwise, that have been fundamentalist and/or radical over the many centuries of the history of Islam.

Al-Qaeda has at its core a political Islamic ideology that is generally derived from the political Islamic ideas of Sayyid Qutb, who was a leading member of the Muslim Brotherhood. If you are interested in where Al-Qaeda really came from, at least ideologically, looking at the history of the Muslim Brotherhood and the Salafi movement is good start.