My older Coachmen TT that I had previously, the furnace was under one of the dining table seats. The exhaust port mentioned above is NOT one of the exhaust vents "inside" the trailer. This exhaust port is "outside"..... This port will lead directly to the furnace. In my current rig, it's located under the kitchen counter behind some drawers.
Also, in my older Coachmen trailer, if the battery was discharged, disconnected and/or removed and even if the trailer was plugged into shore power (120v), the converter would not supply 12vdc to all items that required it. I "HAD" to have my battery connected and charged up prior to ANY 12v item working.
I bet if you put in a charged battery....everything will work.
Hope this helps
Ron