Right! Seems TinyPic are back up - let's have another go -
The inner barrel, right, can suffer from corrosion built up within the handle which will cause issues with fatigue when truning the key. It is that barrel which is in pieces with Ians problem.
Don't forget to replace the circlip (almost out of shot at top), otherwise you will find the barrel with the tumblers coming out with the key!
The sprung plunger if not lubricared can cause the small spring to break, or simply seize up with crud, resulting in a lock that will not unlock, or not lock.
