See a Craig's List Ad pulled up very quickly just now, to give a sample data point of 1 Case. The Ad will expire in a few weeks, and this Link won't work any longer past that. There's also an Avion listed for ~$4k but that's simply a great price IF it's not trashed.
34' Avion Ad
The Ad code words 'needs TLC' means some involved work MIGHT be necessary, but that the asking price reflects that. It also means this Avion would list for more IF that work was already done. Also, there's excellent advice above to post some clear pix here so that a few of us can chime in and attempt to help re: Avion value. 'Free advice is worth every Penny paid', as I like to say!
One major Trailer Manufacturer - NOT to be named here - 'proudly' has a Promotional Video, also on YouTube, showing them cranking out a Particle Board piece o'junk Trailer every ~1/2 hour. Avions were at the opposite end of that Quality 'Spectrum'/Design Philosophy. Unlike Wood-framed Trailers, only something like Chassis/Salt Air corrosion can get an Avion. ~30 years old means nothing in 'Avion World'; they really are Tanks. Case-in-point, look at Craig's List at the prices asked for GUTTED Airstreams, and original or updated Airstreams. The bulletproof Trailer Infrastructure is a major reason Airstreams and Avions hold value vs. lesser, 'throwaway' Trailers. The prices we discuss above reflect Depreciation from the ~1980s price new of ~$22k; SERIOUS money back then for a Trailer.
I've read that the sealed Underbodies can trap moisture and corrosion. I've not checked mine, since it's always been in dry [high] Desert Air. That's something to check if you're going through your Trailer anyway...
My Furnace turns on via the OEM square, mechanical Thermostat. If that doesn't work, and no sound at all is heard from the Furnace when Thermostat-enabled, check the Power Center, and further ensure there's +12 VDC and a good (-) Ground at the Furnace. Mine's below the rear Bathroom Closet.
Also, reset all Avion power. That is, unplug the Avion from 115 VAC Shore Power. Then, flip the front Console Switch above to ensure the Battery Power is off. Then, turn power back on. This would reset Furnace power [and all Trailer power].
I retrofitted a 'Dinosaur' Control Board to my Furnace. After 3 attempts to start the Furnace, it requires such a reset IF both Propane Tanks are empty. This avoids running down both House Batteries. Such a scenario is a remote possibility on your Trailer, but is generally something to be aware of when Troubleshooting. That is, perhaps the Furnace has been replaced or worked on, so enabling the Furnace isn't a Factory-style function anymore. Also, resetting power on just about anything often cures a problem.