Why wont computer boot unless PMU reset is pressed

My sons Power Mac 1.0 GHz Dual PPC has gradually become harder to turn on. At first he would press the power button several times and it would eventually boot. Now, when the power button is pressed the LED inside lights up (goes out as soon as the button is released) but the computer won't start-up. I tested the PMU battery and it is 3.6 volts. I had almost settled on it being a bad power supply and had the whole thing pulled out, then I saw a PMU Reset button on the mother board. I put everything back together, pressed the reset button and the computer started working. However, every time the computer is shut down I have to press the reset and then press the power button to boot up. I really don't know what is wrong now. Obviously the power supply is working. The battery voltage is good. If the logic board was bad I wouldn't think the "Reset" button would make it run. Any ideas?