My guess is case switch wiring or PSU. If your Gateway case has a reset switch, you can swap the power and reset switch and try to boot with the reset switch.
Otherwise, remove the power switch header from the motherboard and momentarily short the two pins together with a small screwdriver.
If that doesn't work, try to borrow a known good PSU to see if it is the PSU. After all this, then it's time to think about the motherboard.