I am not qualified or experienced to offer any worthwhile help with boiler problems... but that has never stopped me trying...
If it fires up then there's nothing wrong with the firing-up controls.
If it switches off after 10 seconds that suggests it's turning itself off for a reason - the most likely reason is that the water is getting too hot.
Either the thermostat that senses that water might be too hot is defective - or- the water really is too hot and is not being pumped away from the heat-exchanger quickly enough or at all.
It is always possible that the control circuit has got itself confused in some way - but I doubt it.
As I say - I know nothing - a qualified boiler engineer is your best solution - do not let him guess at your expense - if he proposes to change something ask him why? Ask him what happens if he changes an expensive item and it does not fix the problem - is his wrong guess your financial responsibility?
A good engineer will make an accurate diagnosis.
Peccavi
January 2013