2006 iMac Desktop computer won't turn on?

My Mac desktop computer from 2006 won't turn on. I tried unplugging it and re-trying and that didn't work. Does anyone know why this happens and how I can fix it?

One time, we brought it in to the apple store and it turned on there so they didn't fix it. Sometimes it turns on randomly after a lot of tries, but now it hasn't turned on for a while. Usually we leave it on, but we had to turn it off because the power was about to go off.

Thank you!!