Remove the little watch type battery from the mother board check the voltage with a meter should be about 3.5 volts. Then replace the battery on the mother board. This battery holds memory within the Bio chips on the mother board, if there was a problem that it sensed for turn on it will be in the Bio's memory, and maybe not allowing the computer to turn on, by removing the battery for a few minutes, the Bio's forget they had a problem, if you will. and the computer might turn on.
If you have all the voltages to the mother board from the power supply, it should turn on.
unless there is some reset circuit interfearing with it turning on. Or you might have a blown fuse on the mother board, I would check everything I could, and try everything I could, and if you still cannot get it to turn on take it to a computer shop and spend a few bucks for them to fix it.