Yyou could do some of the simple things before taking it to the shop. Since you said the batteries went dead, then charged and you've seen the lights flicker, start with cleaning the battery connections at the battery and converter. If they are wet cells make sure they are topped off.
That green blinking light is probably a Charge Wizzard meaning you have a high quality charger(Progressive Dynamics) If all the 120 volt side is fine then the transfer switch is not the problem. The problem is all low voltage if the lighting is the issue.
2019 Horizon 42Q Maxum Chassis w/tag
Cummins L-9 450 HP / Allison 3000
2006 Jeep TJ and 2011 Chevy Traverse Tows