Ok we took them in town and were told that they both were in good shape so I'm not sure but we will definitely get a new one! We were also told that the flame shield didn't matter?
If they were both used by the original owner in the manner you described (trash, pop cans, diesel) they are probably bad. I doubt anyone could say by simply looking at them. The flame shield also matters. It prevents flame impengment of the cat, also bad.
When your stove cools you can open the bypass. Once it's open you should be able to reach about half way back and stick your hand through a hole in the top of the stove. This is the bypass. You can feel for a gasket surrounding the outer perimeter of the hole. If it is there you can proceed to check it by using the dollar bill test by closing the bypass, press down till you here it latch then try to pull the dollar bill out. Due this all the way around. If there is very little to no resistance then you need to move on to adjusting the tension on the plate.