Computer unplugged from power, FOLLOW Anti-Static Precautions.
1) Remove the Side Panel.
Viewing the computer from the Front; the Right Side Panel removes. Remove screw, pull Side Panel to the rear of the computer.http://www.newegg.com/Product/Product.aspx?Item=N82E16883113140
Click on the large main photo.
There are 9 smaller views shown. 3 across, and 3 rows.
Bottom row, click on the photo in the Middle.
Shows Rear view of computer.
Along the back edge of the Side Panel, is a finger pull handle formed out of the Side Panel. There also looks to be two screws. One above the pull handle, one down towards the bottom.
2) Remove the Front Bezel.
Click on the Middle row/middle photo.
Also look at Middle row, 3rd photo. (Photo all the way to right)
There are 3 Black tab locks, formed out of the plastic of the Front Bezel. One towards the Top, one in the Middle, and one towards the Bottom.
If memory serves these tabs are gently pulled to the outside, to release the Front Bezel. Ease the Top tab out a little, and Middle tab.
Start easing the Front Bezel away from the metal framework, of the computer case, a little. Then release the Bottom tab.
Front Bezel should swing, and then come off.
Not your Gateway model of computer case, but this Gateway model shows the plastic Tabs to release,http://support.gateway.com/s/CASES/3501975/3501975faq6.shtml
The Power On Button is an assembly. The plastic housing of the Power On Button assembly, has a Power On switch inside.
I gently heat the plastic with a hair dryer, moving the hair dryer back, and forth at it.
Once the tabs of the plastic, of the Power On Button assembly, is softened; then I remove the Power On switch.
I have found this ATX power on switch, fits a LOT of desktop computers,http://www.directron.com/atxswitch.html
For additional questions please post in a Comment.