After water spilled on the cooktop and leaked into the knobs, both the LED lights and spark ignition stopped working. After a little research, I determined the likely cause was a short in the switch which blew the transformer. I ordered both the switch harness and transformer (super-fast next day delivery at the standard rate!). The replacement was easy. I was a little nervous because the replacement switches are different from the original, but they all fit perfectly. The stovetop is working again - even better actually because I took the opportunity to clean all the burners and gas jets.
Thanks!