Turns out we don't have to buy a new stove after all because my husband can fix almost anything, and I mean that quite literally. He did a few tests with meters and other gizmos he uses in diagnosing a mechanical or electrical problem and found out it was a switch thing that tells the big flame when to go on and off. He went to the parts store and bought the part and it was working within a matter of minutes, and the house is still standing. Now we can still plan to buy a hot tub. :-)
The part for the stove fits in the palm of your hand and cost $100!!! It must be because I am getting old, because the price of things today just astound me!