The leak is caused by the rubber seals inside the mixer unit in the processor.
If you are handy using a philips screwdriver you can remove the cover. (don't forget to turn the water off on the inlet pipes) Open the mixed unit by removing the two philip screws that hold the collar in place.
Inside there is a metal disk (this is the mixer) underneath are two washer that fit over two springs when these stick the water continues to flow.
Remove them by pushing them into the socket they should then pop out. Once out apply silicone grease reinsert and put everything back together.
Sounds like a faulty PCB inside the digital processing unit, unfortunately this is not available as a spare and you have to buy the complete processing unit.
http://www.showerdoc.com/aqual-223118-aqualisa-pumped-digital-processor-(grey)-223118
This unit has a 5 year guarantee so check that it is not still within the guarantee period.
If it is less than 5 years old then it is still under guarantee if it is older then you are going to need a digital processing unit.
Which unit you need will depend on which model of Quartz you have.
Unfortunately yes you need a new processor as there no user serviceable parts inside the processor.
However remember that this unit has a 5year guarantee
The Aqualisa Quartz Digital shower is a current model and can therefore be easily replaced