How old is the house? I ask because the wiring is not up to code. There must be two separate circuits to your kitchen countertops and they must be GFCI protected. It sounds as if that circuit extends past what is normal.
Anyway, it seems to boil down to the wiring in the range hood. Remove the power at the breaker and pull the cover off the connections in the hood. If the shorted wires are still touching each other, it will cause what you are describing. Separate and make sure the exposed ends of the wires are properly capped, then put them back in the box. You may encounter a black flashed area where it occurred. Let us know how it goes.
Anyway, it seems to boil down to the wiring in the range hood. Remove the power at the breaker and pull the cover off the connections in the hood. If the shorted wires are still touching each other, it will cause what you are describing. Separate and make sure the exposed ends of the wires are properly capped, then put them back in the box. You may encounter a black flashed area where it occurred. Let us know how it goes.