Your 2013 RV Unit should have the smart mode type converter/charger in it to keep your battery from boiling out fluids. My 2004 5th wheel only has the single mode converter/charger in it and I have to keep watching the battery for boiling out fluids. If you don't have the multi-mode type converter/charger or using a WFCO product you would gain alot by replacing the converter/charger unit to a Progressive Dynamics or IOTA model converter/charger unit. They always works and the WFCO products are known not to do that for you...
I suspect just sitting and maybe not plugged-in has done your battery in... My battery would only last a couple of weeks being discharged by the so called parasitic drains... The rule of thumb to run your furnace when off-grid is one night for one battery. My furnace blower draws around 6AMPS DC current when running.
If you are plugged into shore power then the converter/charger should be giving you the 12VDC you need to ignite your furnace...
The Battery is your lifeline and like the rest of us keeping a close eye on the battery really pays off in the end... When they get discharged below the 50% charge state (Around 12.0VDC) then they kinda act like your car battery holding a charge - not good indeed...
Let us know what happens after getting a charged-up battery back in the system.
Roy Ken
My Posts are IMHO based on my experiences - Words in CAPS does not mean I am shouting
Roy - Carolyn
RETIRED DOAF/DON/DOD/CONTR RADIO TECH (42yrs)
K9PHT (Since 1957) 146.52M
2010 F150, 5.4,3:73 Gears,SCab
2008 Starcraft 14RT EU2000i GEN
2005 Flagstaff 8528RESS