If you've left it unplugged all winter, then the batteries were likely completely discharged and probably shot. A fully charged battery will not self discharge too much during a winter if it is completely disconnected from any loads. But if left connected then you have parasitic draws that put a small but continuous load on the batteries. In my Aspen Trail they are the propane detector and stereo. This make take several days to discharge a full battery, week or more and the batteries are severely discharged, over months and the batteries have been killed beyond recovery. Mine did not have any sort of battery disconnect so I suspect that your's did not either, but having it engaged is a good idea from other posters here that might describe your issue.
Now while I stand behind my suspicion that the batteries are fully discharged and probably shot, I cannot explain how the slides would work but nothing else. Slides operate on 12V power, so unless you're plugged in to shore power then they should not be working with dead batteries. If you are plugged in now but weren't all winter, then the converter would be powering the slides with 12V but I can't explain why nothing else 12V works. I would suspect burned fuses like other posters mentioned. Maybe the big current rush from the converter when trying to charge wrecked batteries blew a fuse? wahoonc has a good thought with a nonfunctioning main inline fuse but directly wired slides. These fuses are usually auto-resetting, but maybe it isn't working right. That would explain the symptoms.
If you're using the push button battery status meter that comes with the camper, it isn't telling you anything useful when plugged into shore power other than the converter is functioning. It will show full charge, because the converter is supplying a continuous 13.6V to the system. But the batteries may be anything from nearly dead to fully charged.
The fridge works on 120V AC and propane with 12V. So when not on shore power, you need both 12V and propane for it to work. 12V powers the control board with a continuous ~1 amp DC draw, so this is another parasitic draw on the battery system while you are running the fridge.
2012 Aspen Trail 2710BH | 280 watts of solar on the roof | 2x6V GC batteries | 100% LED lighting | 1500 & 300 watt PSW inverters | so far strictly boondocking