The green wire on the PSU-Mobo (20-pin) wire will start the PSU up. But not the motherboard.
The power light, hard drives, possibly even graphics card, will fire up, but the CPU won't begin ticking until the motherboard tells it to. You can't just GIVE it power, it needs to be ready to turn on.
If you are good with circuitry, you may be able to trace the tracks along to the source of the problem, and trigger a power-on beyond that point.
Actually, having read some stuff it MIGHT work for you. Give it a go!