I do not think there is anyway to open up your button control panel. Since it is only one button, and not multiple unresponsive you will probably need to replace the entire panel, rather than the electronic control 'mother' board inside. You can fix it quite cheap, without needing a repair person.

It's actually very easy, after opening the back of the door, you just need to unplug a few parts detach the piece (control 'mother' board, a few plastic tabs and other wiring all with simple plug ins), reattach new piece to door and reattach parts. After disconnecting from power source of course.

It only took us about 20 minutes, start to finish and we had never repaired an appliance before. The hardest part was finding the tool to open the door and remove the control panel! No one knew what we were talking about (and I never did learn the name of that special wrench!), I ended up bringing a cell phone photo of the screw I needed to remove to an Ace Hardware.