For the furnace the battery only runs the blower,
Not true. The battery also runs the electronics on the furnace, including the igniter. It's possible that with the battery somewhat depleted, the current draw by the blower was enough to lower the voltage at the electronics enough that they died.
But given this was your first time to light the furnace ever, I'm guessing your problem was air in the gas line.
1988 Coleman Sequoia - popup (1987-2007)
2012 Roo19 - hybid (2012-2015)
2016 Mini Lite 2503S - tt (2015 - ???)
2011 Traverse LT, 3.6L, FWD
2009 Silverado Ext Cab, 5.3L, 4x4, 3.73
2016 Silverado 2500HD Dbl Cab, 6.0L 4x4, 4.10