Calciopoli allowed them to establish domestic dominance for 4 seasons and also take some of our players (Ibra most notably). They had an excellent base for Mourinho and with the Ibra sale allowed him to build his ideal team. They also got lucky, Chelsea were without Cech, A. Cole, Essien and Deco, then CSKA in QF, offside goal vs barca and Bayern without Ribery in the final.
The problem was, that was Mourinhos team as it was built for him, so when he left it started falling apart. Didn't help that all their leaders were old and were on their last try. moratti also lost the desire to keep investing as he reached his goal already, hence the decline.