The first step in troubleshooting a computer that does not turn on when the power button is pressed is to check if there is any power going to the computer. The technician should reseat or reconnect the power cable to ensure it is firmly attached to both ends, and confirm that the outlet or power strip is providing energy by using a multimeter or another device. This can eliminate any issues with loose or faulty connections or power sources, and help isolate the problem further.