Delonghi ESAM3500: - Cannot turn machine on using power button. Turning off and on at socket goes into self-diagnosis. Two whirs of the motor then it shuts down again. Is this fixable or time to throw my expensive 3 year old machine out?

It is the normal behavior that when you plug the machine in it does the self-diagnosis (with the 2 brief motor sounds) and then goes quiet, simply displaying the clock. If this is what you see but the unit doesn't start up when you hit the power button, I'd first suspect the power button itself or a problem in the set of wires that connect the buttons to the main board. Unfortunately, to test this, you'd need to open up the machine and start poking around - something not everyone is inclined to do... It is the normal behavior that when you plug the machine in it does the self-diagnosis (with the 2 brief motor sounds) and then goes quiet, simply displaying the clock. If this is what you see but the unit doesn't start up when you hit the power button, I'd first suspect the power button itself or a problem in the set of wires that connect the buttons to the main board. Unfortunately, to test this, you'd need to open up the machine and start poking around - something not everyone is inclined to do...