Sadly, the old and busted cooktop is old and busted. The new hotness cooktop, provided by the internet, will arrive in about a week. Everybody wanted at least a few days to get one I liked from their warehouses, and Lowes actually told me two weeks. Do these people not realize that it's 2009? I could have my robot butler drive up there in my flying car and pick one up in a couple of hours, guys. Step up your game.
The circuit it blew is back online now as well. As so often happens in my household, it was a simple matter of taking another look at things and making no assumptions. My dad observed that my grandfather's house has the same steampunk fuse boxes as mine does, and the last time they blew out a circuit by plugging in their new miracle space heater from the TeeVee, they went crazy trying to figure out the problem. In the end, they replaced all the fuses just in case, and it started working--even though they'd all been checked. You see where this is going? The plug fuses, which look like this, were just fine. You can check them easily; if the circuit shorts, they fill with black smoke and you can't see the element. If they overload, the element breaks. If you can see the intact element, they're still passing current.
But the cartridge fuses, which look like this, are more difficult. I put a continuity tester on those, and they were dead, so I bought a couple of new ones and voila! The power, she flows. Now we have an oven again.