Alesis' digital effects are computers designed to process sound information basically like all the other digital effects. They use a lot of specialized chips of course.
Usually power supply or solder problems that I've seen on these. Here is a good tech page on the Midiverb II.
Advanced Musical Electronics has a lot of parts for Alesis stuff. THey only deal with techs though.
I've also seen All electronics carry displays occasionally at low prices.