The button you talk about is the reset button for resetting the overheat thermostat - an important safety device to stop the boiler exploding - as you say your boiler used to overheat so you used the button to reset the cutout.
Now the boiler is no longer overheating and you don't need to mess with the reset button because the overheat thermostat has not tripped out - the reset button is floppy - it has nothing to reset.
When there's a call for heat the fan runs and activates a pressure switch in the cabinet - only then will the pilot flame appear.
You should hear the fan running - if you don't hear it then that's the cause of no pilot flame - if the fan does run then it may be the air pressure switch - or a badly operating fan - or a leak in the cabinet - or perhaps (unlikely) a defective control board.
If you do call in a specialist it's doubtful that there will be more than one defective part - he may be guessing what to change or he may be changing things just to help his profit margin.
You can safely ignore the Overheat Thermostat and its Reset Button for the problem you describe.
Good luck...
November 2014
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