1) If you're a tennant then the landlord is respoonsible for repairs - if you tinker with the boiler (beyond the user controls level) he could hold you liable for the costs of any future repairs.
2) You will know as an engineer in electronics that equipment such as a gas boiler can not possibly have a mind of its own - equipment either works, does not work or has an intermittent fault.
3) When the boiler gets a call for heat the fan is started - a pressure switch senses the correct pressures in the sealed unit and signals the control electronics. The PCB causes the pilot electrode to spark and opens the pilot gas valve. A heat sensor monitors the heat of the pilot flame and signals the control board which opens the main gas valve and the boiler fires up. If the pilot fails to ignite the fault may be fan, case seals, flue, pressure switch, PCB (not recognising pressure switch, failing to make spark or failing to open pilot gas valve) or the pilot gas valve not operating.
If the pilot flame does light but the boiler not fire up the fault may be: pilot flame too feeble to properly signal control board, heat sensor not working, PCB not recognising or acting on signal from heat sensor, and most often, main gas valve not working.
Boiler engineers who are not too clued up on diagnosis sometimes change bits at random - generally they do not understand electronics and will often change the PCB on "spec.".
4) If you have a hot water storage tank it should ideally have an immersion heater in it for emergencies such as yours - your new property with a combi will not have such a luxury and bath filling will take longer than you might wish especially in the winter when the incoming water will be cooler.
5) Much will depend on the pilot flame on your boiler - if it's coming on and you have to wait for an extended and variable period before the boiler actually fires up I would suspect the pilot injector being partially blocked and not producing a big enough flame to trigger the next stage - I only offer this because this is what happend to my Potterton boiler which, at the time, appeared to have a mind of its own.
Good luck...
Peccavi, May 2009