2000 Northwood Nash 22h fridge and inverter issues

Hey guys! I have a 2000 Northwood Nash 22h that I'm having a little trouble with. I have checked the fuses and breakers inside the electrical control panel. I have checked the 30a fuses on the inverter, and the 2 fuses (3a and the glass tube one) on the back of the Norcold n621 fridge.

I can't get the fridge to work on shore power, only on battery. The fuses all look to be intact everywhere. I have tried the propane but I'm out so the pilot doesn't light.

Also, it seems like the inverter isn't powering or charging the batteries well either. I'm just looking for a little help or guidance.

Oh, and last year my Coleman Mach started smelling like burning rubber when the ac would kick on, but a friend of mine is thinking that it's a capacitor. Looking to see if anyone has any guidance for that as well.

Let me know what you think is going on!