B
Billy Bob Bob
With a dodgy thermistor the boiler will light for a few seconds then shut off. It won't show any faults.
Sounds more like the pot is knackered especially if it has been used to turn the heating on and off for the past however many years. It is not designed for that.
If you are into electronics you could probably source one and fit it to the board.
I hope your folks have some other kind of heating as it is still 4 weeks (gawd is that all) to christmas!
good call tamz could be the pot never seen one fail though,mind it is a ferrolli though TBF the boards Honeywell seen loads of the resets break