I am not a boiler engineer but...
The symptoms you describe are symptomatic of an intermittent electrical connection - sometimes good and sometimes bad. Heat and vibration causing the connection to be made and not made with no pattern to the failure mode or the correction of it.
Try striking the boiler to encourage it to work - if this is successful then it strongly suggests a bad connection somewhere inside.
If you are able to operate it with any of the covers removed then use a wooden spoon to gently tap around to try and discover the area of the dodgy connection.
If you are able to remove and examine the control electronics you can check for poor soldered joints on the pcb. A digital photo' helps with reassembly.
Here's a picture of a dry joint...
http://s133.photobucket.com/albums/q43/randallembers11/?action=view¤t=dfd.jpg
All this is guessing and no warranty is expressed or implied
Good luck...
Peccavi
March 2009