Sarah,
I know nothing about repairing stoves with the pushbutton controls, but I would imagine that the replacement parts may be more difficult to find,
I have replaced the infinite controls on a couple of stoves and its was easy-peasy! Just order the right control, pull the range out from the wall, either turn off the circuit breaker for the stove or unplug it from the wall, remove the back of the control panel and unscrew the old control from the panel. Then just remove one wire at a time and connect it to the same tab on the new control and repeat with each wire,(or take a picture of the connected old control with your phone or iPad so you’ll know the correct way to connect the new one) screw the new control onto the panel, replace the back of the panel, plug the stove back in or turn the circuit breaker back on and move the stove back into place. It takes 10-15 mins start to finish.
Eddie