Yes, they should be fully charged if you've been plugged into shore power for several hours. It sounds to me like either your converter, or inverter ( not sure which you have) is not charging your battery or your batteries are "shot".
Have you checked the water in your batteries? Is the water at the proper level?
How old are the batteries? If it were me, the batteries would be the first thing I'd have checked out. If they are good, the converter/inverter may be bad.
Days camping (2015)----88 days
Days camping (2016) ---110 days
2016 Wildcat MAXX 28RKX (33' TT), 2007 13' Scamp
2015 Ram Laramie Hemi
30 years RV'ing
12 different RV's