If you've had a "deep" rodent infestation, you have work to do. I'd suggest that you pull the under belly coverings and start inspecting ducts. There is a good chance that you have nests and debris inside the ducts. Probably some holes, as well. Critters play havoc with this stuff and it's not just what you can see/smell on the surface.
Have you used the oven recently? You may be in for a surprise when that heats up, mice love to get into the range and setup house.
BTW, those two openings you've found in the exterior are the fresh air combustion intake and the combustion exhaust. They lead to the burner chamber and are not connected to the duct work.
