Your mileage will vary, but I was a bit stretched when I bought our house, and the idea of remodeling the kitchen was far from my mind at the time (I've since built a small addition, and I'm in the process of remodeling the kitchen and dining room, but that's 12 years later.) I'd have been put off by a broken cooktop, and it would immediately make me wonder what else was broken that I couldn't see. So I'd rather see a decent, working cooktop.

i would go the cheapest route and just repair it. no sense throwing away more money than you have to. if you planned on staying for a while i would replace the whole thing, but not for just a few months.

I would also just repair the part, it would make your life easier while you are still there. let the new owners re-do the kitchen they way they want to after they move in. in the meantime they have a stove that works.

Find a used appliance shop and get the part. You can probably make the fix for under $50. Just take in your old part along with the make and model.

I have done this to replace electric stove top elements that stopped working at a fraction of the cost.