Replacing the control panel assembly is extremely easy with one exception. To take off the existing panel (and there is no way to order a button for this, you have to order and replace the entire assembly), you pull the dial knob off (it comes right off, no tools required). There's a single screw underneath, Phillips head. You can then slide the panel up, and then unplug the cable connecting the circuit board to the dryer itself.
Next steps: Unscrew the half dozen or so screws to remove the circuit board from your old control panel. Use the same screws to attach it to the new panel. Then unscrew three screws from the top of the old panel, there's a long rectangular top you'll need to place on the new one since it isn't included.
You now are 100% complete except for the GE logo which does not come with the replacement assembly. There's a little tab on the back that attaches the logo, I pushed it out with a small needle nose pliers. This was very difficult, as it was also secured by an adhesive circular piece of tape that was strong, and invisible.
My biggest issue with the entire process is cost. Applianceproparts.com is great, they were cheaper than GE and fast to ship (with affordable shipping upgrades). It's just absurd that GE won't sell the power button separately, on a part that casual Google searching indicates is very prone to snap off, so I'm $180 in to replace a oval button. If the $180 came with the circuit board, I'd at least understand the price, but it's literally plastic, and doesn't even come with the logo. Just a shame to drop $180 into a dryer that was under extended warranty (but had "cosmetic damage not covered", that only cost $699 in the first place. That said, if you get stuck having to do that... do it here, this is a great site!
Please note my five star review refers to the great guys behind this site, the quick shipping, the well packed item, and the relatively simple repair. My review of GE relative to the price of this part, the design of this button, etc is more like a 2.