Changing the control box would appear to have fixed the problem but I’d like to chuck a couple things in. As said above the white motor wire returns roughly 50v ac to control box, this is used to power the rest. You say you felt little magnetism when using the screwdriver trick on coil. I use a electromagnetic field tester or solenoid tester if you will to check it’s function, remember these Riello domestic burners supply low voltage dc to coil which is why they use the metal bracket around coil to improve the magnetic strength, just bare that in mind in future as it’s not unheard of for custards to fiddle and it may have been misplaced, although they’re usually solid. The RDB coils are virtually bomb proof, you may need to change one from time to time but probably never two or three lol. Also when checking fuel to nozzle I would disconnect cell from control box, remover ht leads from electrodes and remove blast tube and aim burner into collar when proving atomisation of fuel at nozzle. As said above someone who works on oil regularly should have plenty of van stock to fix these things first visit.
Anyway glad it’s fixed