I'd suspect the power supply first, but my experience with Gateway has been that they use very flaky components. As a circumvention, you could try using hibernation instead of complete shutdown. I bought a Gateway desktop in 2006 and within weeks the keyboard crapped out. Then after a year's use the monitor went. Shortly after 3 years the system wouldn't boot and Gateway didn't have the parts to fix it, so they referred me to a 3rd party that wanted $200 for a motherboard. I removed the hard drive and put it in another desktop I built and have avoided Gateway ever since.
My gateway will not always boot on the first push of the power button when attempting to start after the computer has been turned off for several hours. Have no problem starting the computer shortly after it has run. The computer will at times boot on the first push of the power button, but most alway will require two to three attempts.
Can anyone help me with this issue.