We had a similar situation when our kids were younger.
We have  a Stoves oven  (720EF with 5 timer buttons) and I think what happened in our case was  the timer gets  set somehow to switch the oven ON at an unknown time in the future (This is perhaps why your oven will not switch on manually ) .IIRC switching off at the mains for 20 minutes and then switching back on cured it .(One other regular reset I do remember when we couldn`t get it to work after the kids had been "playing" was pressing two of the timer buttons at the same time.)
Not really an answer , but at least something to try.
In the end our  timer failed ( the display failed and the alarm kept buzzing when not used  ) so I had to dismantle it and overwire/strap  the timer out to keep the oven working. It`s still like that as a new  timer circuit board was going to cost around £125
It just means that we cannot set the oven to Automatic...but we rarely need that as the kitchen boss is at home all day.
Good Luck
                
 Mike
                
 November 2009