The humming could be the fan seized. there is a sequence of operations which leads up to safe ignition of the main burner. Once the sequence has started it has to test the fan is running , the spark is good enough and the gas is right .only when everything is right will the burner ignite and carry on runing safely.
You can only go further in to your boiler if you are corgi registered because it involves gas and products of combustion.
Call an engineer. No other legal option at this point.
Terry
May 2007