Are you aware that some motherboards have 2 power connections?, I also had a no power problem after building a pc, only to find that I had only used one of the power connections. Once I connected the second smaller one I was up and running.
"Could the on/off switch be knackered?" - yes, could be. Try 'shorting' the motherboard headers (with a screwdriver or similar), where the on/off switch wire attaches to the motherboard (small trick learnt from woodchip). Please be careful - you need to short the correct ones. G