I have the same Cuisinart toaster with a different problem. In taking it apart to try and fix it, I may have gained insight in to fixing your problem. If your are willing to get under the hood of your toaster, you might try working with the electronic contacts that the function dial controls (it might void a warranty, but since you are out of warranty period no problem):
1. Unplug it from the wall
2. Remove the stainless steel case from around the toaster via the small screws around the toaster's bottom, sides, back and the black screws at the top just inside the door. This should allow you to see the electronics behind the dials.
3. Look at the function dial. by turning it you are turning a white plastic cam which presses down different combinations of metal electrical contacts to make the functions work. I suspect there is something wrong with the contacts that are pressed down to control the "BAKE" function. Turn the function dial to "BAKE". and Check the contacts that are pressed down by the cam.
4. Are the contacts free of crud or corrosion? If not, try cleaning them with a small brush or q-tip with CLR or some other rust remover or degreaser. After cleaning let them dry and plug in the toaster (once plugged in do not touch the electronics!) and try "BAKE" for a second. Turn it off and unplug it. If it works, reassemble. Otherwise try step 5.
5. Are all of the contacts pressed down by the cams completely in touching the metal on the plate like they are supposed to? If not, try bending them so they will touch when closed by the cam (but remain open when the cam is not pushing them). Are the contacts free of crud or corrosion? If not, try cleaning them with a small brush or q-tip with CLR or some other rust remover or degreaser. After cleaning let them dry and plug in the toaster (once plugged in do not touch the electronics!) and try "BAKE". If it works, unplug it and re-assemble.
6. If its still not working, email me (firstname.lastname@example.org
). Maybe I can help. I am also willing to buy your toaster so I can fix mine.