I was able to fix the start button issue using the great comments above. Thanks for posting them.
A few things to add that might help.
I replaced the Control PCB Assembly with a new assembly from eReplacementParts, using the link above (part number SP0010507, for $41.03). The part was backordered and took 2.5 months to arrive. The new screen is bright and the start/stop button works every time; feels like new. I did not solder.
I used both methods described above (by Chris and Phil). I used Chris’ method first. I was actually not able to fully remove the top case, only the left side of it (when looking from the back); the black screws were definitely a challenge.
Later, I read Phil’s method and decided to give it a try. For me, the top and right sides of the top case were held in very tightly, so it took a lot of wiggling and a fair bit of force, to finally pull them free. Remember to remove the screw on the bottom of the oven first. The top and right sides have a tongue-and-groove fit with the front of the oven. And, it also wasn’t the easiest thing in the world to put the tongue back in the groove when re-assembling. Note that with Phil’s method, you do not have to remove the back of the toaster oven.
Once the top case, with the control panel still attached to it, are free, and the two wires are disconnected, it’s easy to remove the black screws, as Phil says. So, having tried both methods, I would use Phil’s if I had to do it again.
One final thing. When I removed the white plastic cover from the control assembly, a spring fell out. I assumed that it fell out from the start/stop button and that’s where I put it back when re-assembling the control unit.