oldblue99
It is possible, just possible that you can salvage the board. More than likely it was the last thing you changed that caused the problem. The last thing you changed was the resistors from Radio Shack.
Liklely cause of "smoke" is that the resistor was rubbing or sitting against some other part and eventually caused a short. Or, it came loose, fell and lodged against another component causing a short. An open circuit will not burn nor smoke, but a short circuit will cause current to flow where it is not supposed to and burn up.
I would remove the board, and examine it very carefully. You should be able to see and/or smell the area or part that burned up. And with some luck repair it back again. If the circuit board is damaged, you can most times jump the burned run with a piece of wire... just make sure you get a clean connection.
This problem of "smoke" should not affect your mileage - this DIC board only displays the mileage, does not compute and store the mileage.