Welcome to the forum
Your TV and PC are 110VAC appliances. Your lights, furnace and fridge controls are 12VDC appliances.
Your converter will take 110VAC and produce 12VDC to power the 12V appliances and charge the battery.
You need to locate the converter and using a Volt/Ohm meter, determine the output. There is also 2 fuses located on the back side of the converter or off to the left of the row of 12V fuses, called reverse polarity fuses. If you changed your battery and hooked it up backwards for even an instant those fuses will blow.
Check things out and post back.
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2012 Copper Canyon 273FWRET being towed by a 1994 Ford F350 CC,LB,Dually diesel.
Airlift 5000 bags, Prodigy brake control, 5 gauges on the pillar.Used to tow a '97 Jayco 323RKS.
Now an RVIA registered tech. Retired from Law enforcement in 2008 after 25+ yrs.