Thanks for the tips, guys!
Couldn't find a manual, but decided to tackle this today. To get the top off this unit, I had to pull it out of the surrounding cabinetry, and undo two screws in the back top, then push the top towards the back and lift the back up. Tricky, but doable.
Luckily, it appears to be a simple problem. One of the female spade connectors on one of the wires for the switch for that burner had fried - the plastic insulator over the connector had melted to a black mess. Not sure why, although it looked like something had spilled down into that area at some point in the past, so perhaps it finally reached critical mass. Went down to the local Fry's to get a new insulated connector, snipped off the old, attached the new, reassembled, and it seems to be working fine now.
Scary bit - the circuit for this stove does not have a circuit breaker in my breaker box. Tripped all the breakers, but it still had power. Managed to reach the power cord and unplug it after I'd removed the lower drawer below the oven.
Tips for amateurs like me:
1. Raise the unit - if your stove has a lip that goes over the edge of the surrounding countertop, and you have adjustable feet on your unit, give each foot a few turns before you slide it out. It will be gentler on your counter top since the lip won't be resting directly on the counter top while you're wrestling it out.
2. Beware the marble - if you have marble countertops, be gentle. I thought I was being gentle, but apparently not, and broke off a section of what I'll call "under-lip" - the lower half of the rounded front edge of my counter. Now I have my next project...