The actual theme starts at 3:25. The Godfather Theme has been one of Slash's signature concert songs since the days of Guns N' Roses, and has varied in length over the years. These days the solo will frequeantly last 10-minutes, usually with a few minutes of bluesy stuff or random improving at the beginning, like in this video.
Also, for those of you who have listened to his latest album Apocalyptic Love, you'll notice he plays the riff to one of the songs at 7:28. Figure out which one!