How can I tell if it's the I/O board or the motherboard?

Hi Robert The motherboard will usually start up the fan and if there's a problem it cuts off . Is there any lights working anywhere the boards are 5volt dc the IO board is hard to test but it is possible the MB is easier but you may have voltage and the boards faulty if its the MB then it will usually try and start then go off if its not starting it may be more like the IO which is much easier to replace you need see if 5v are there and what's lighting up on start or not.

The button which turns on the laptop there is 2 connections at either one there should be 5 volts you need to find a ground to test accross it will be one of the others on the ribbon cable you need to find it if you get a cct diagram of your switch itl be colour coded or you need try them all with your button connections both sides unless you know which is the supply one a diagram would be best and watch you don't short anything also a diagram of your MB and test it to itl give you +5v and your ground 0v these are the points your looking for its often difficult to get this info manufacturer maybe best