Thanks for the quick reply! Any idea how to tell if the wire gauge is good enough? I assume if it's a 20 amp breaker, then the wiring is probably up to handling the new 20 amp oven (I worry that the current draw of a new modern convection oven will be higher than a 20 year old oven, but it might actually be less given modern materials...)

I'm not sure about the WWII copper shortage. That's just the "story" I heard. Doesn't change the safety issue. Here's an excerpt from a website that attributes the 3 wire "legalization" to the post war housing boom. A little dubious because 1947 seems to fast after WWII for a housing boom. http://www.dli.mn.gov/ccld/PDF/eli_GFCI_history.pdf Circuit grounding was one of the more hotly contested topics in the early history of electrification. In the early 1890Âs, the New York Board of Fire Underwriters had condemned the practice of grounding the neutral as a dangerous practice, especially in a 3-wire Edison (120/240 Volt) system. The Edison utility companies, on the other hand, found just cause to ground their supply systems, even as others thought the utilities were doing this to just save copper and money at the cost of an increased fire risk. The great debate continued for over a decade, but in 1903 the Code was revised to recommend that these circuits be grounded, and finally in the 1913 Code a mandatory circuit grounding requirement was included for circuits like the popular residential Edison 3-wire system. The permission for neutral grounding, the practice of using the neutral conductor as an equipment grounding conductor, was first permitted in the 1947 Code for electric ranges. At around that time many electric utilities were promoting the use of residential 240 V cooking for the post WWII housing boom, and many were even offering to install an upgraded service to older homes at no charge. However, there were no NM cables available at the time with conductors of sufficient ampacity to handle these higher amperage branch circuits. There were, though, service entrance cables of sufficient size, but they had a bare neutral conductor. This special Code permission allowed the frames of these large appliances to be grounded through the uninsulated grounded neutral conductor of the Type SE service entrance cable used to supply the branch circuit. The use of neutral grounding was also extended to electric clothes dryers in 1953. However, almost 50 years later, this special permission for neutral grounding was taken away in the 1996 Code for all but existing branch circuit installations.

The fact that the new cooktop did not work when you connected both the white and bare wires from the cooktop to the bare wire from the supply cable means that you have a bigger problem with the house wiring itself. (It should work) Your entire grounding system could be messed up. This can effect the efficiency of other safety measures in the electrical system, such as the breakers may not trip when necessary, resulting in a fire. You need to have this fixed by a qualified electrician who has the ability to track down the problem. Then, you can keep the cooktop too. The next one you try may not work either. 250.140 Frames of Ranges and Clothes Dryers. Frames of electric ranges, wall-mounted ovens, counter-mounted cooking units, clothes dryers, and outlet or junction boxes that are part of the circuit for these appliances shall be connected to the equipment grounding conductor in the manner specified by 250.134 or 250.138. Exception: For existing branch-circuit installations only where an equipment grounding conductor is not present in the outlet or junction box, the frames of electric ranges, wall-mounted ovens, counter-mounted cooking units, clothes dryers, and outlet or junction boxes that are part of the circuit for these appliances shall be permitted to be connected to the grounded circuit conductor if all the following conditions are met. (1) The supply circuit is 120/240-volt, single-phase, 3-wire; or 208Y/120-volt derived from a 3-phase, 4-wire, wye-connected system. (2) The grounded conductor is not smaller than 10 AWG copper or 8 AWG aluminum. (3) The grounded conductor is insulated, or the grounded conductor is uninsulated and part of a Type SE serviceentrance cable and the branch circuit originates at the service equipment. (4) Grounding contacts of receptacles furnished as part of the equipment are bonded to the equipment.

More info, if it helps: I have a very 'straight, flat roofed' stucco house, with no soffit or crawlspace, unfortunately. I'd 'like' to take the cable outside and down in PVC, and then run UF along the base of the stucco at bottom. It could go out the exterior portion of the service panel (a horizontal extension). But shouldn't it stay in PVC down to the base of the stucco, or perhaps use UF cable without PVC (once it reaches the lowest base of the stucco) to go around the outside corner and down to the needed spot? Because it is stucco, I hope to run it outside first, but have to decide the best way to route the cable (or wires in PVC) around an outside corner to the wall on the side of the house. Otherwise, I believe it has to go 18" down in a trench in PVC, or using UF. But stapling UF to the base of the house is easier, I think. Thanks again for all help!