Matt,
The refer has some fuses in the back of the refer compartment accessible from the outside, lower vent. Some are glass fuses in black holders and others are blade style. the blade style fuses are behind a black plastic cover behind the refer.
While the refer can work off 110 volts AC power or Propane gas, it still requires 12 volts DC to control some items (control board, I think and the heater wire if you have an ice maker).
The furnace, if it's the standard Suburban we normally use, requires propane and 12 volts DC. It does not run on AC power.
None of this gets you going, just arming you with a little more information.
You mentioned that you turned off the refer. Try unplugging it from AC power as well, just as a quick test. Behind the refer, behind that lower vent cover and usually to the left is a single receptacle with the refer AC cord plugged into it. You can unplug it for your test.
I agree with the others that it does seem odd that the refer and furnace share a 12 volt fuse in the fuse panel. If you can't get hold of your dealer, try Heartland Customer Service at 877-262-8032. Also try Suburban at 423-775-2131.
If you don't have phone service, troubleshooting via email with your dealer, Heartland or Suburban is going to be hard to do.
Best of luck to you.
On edit: I looked at the Suburban website and
one of their FAQs mentions that low voltage can be the cause of a furnace to not work. Check your monitor panel to see if your battery condition is excellent. If you are plugged into shore power, the converter should be charging the battery and the top light on the battery condition should be lit. If your battery level is lower, you could be onto something.
If you don't have ready access to it, for reference, the Suburban manual can be found on the Heartland Owners Manuals site
here.
Jim