We have a little toaster oven that I bet would bake cupcakes!
Our oven doesn't work either.... at least the bake doesn't work well, never seen it get above 200 degrees. The broil works real well, so when we've had to make it work, we just alternate the broil and bake until whatever it is gets sortof done.
I had a toaster oven that did make brownies and cupcakes... it broke too (it was very old).
I bought another one and it didn't do so good...burned the top, inside still runny. But I think it's just the particular type. I'm returning it and looking around for a better one.