Lights on but computer would not boot

Ahh Saturday. This computer's lights came on but it would not boot. We can't test motherboards directly but we can test them by a process of elimination. First I remove all peripherals - Memory, data cables to the drives, graphics cards and any other cards. Then I attach a new power supply (PSU) to the two power connectors on the motherboard. 80% of the time I'll get the computer to boot. This case however the motherboard was dead and the customer decided she would rather buy a new computer.