If your plugged in all the time it sounds like you potential have a couple problems adding up to cause this:
- First check your battery water level and make sure you haven't dried them out
- check your converter output for something like 13.6 volts. Your converter sounds like it has failed and not charging batteries
- I also sounds like your disconnect switch was left one which caused the current to drain the batteries without the converter working
- since your engine battery died too, your system isolator might be stuck closed as well
- How big is the solar system? If it is small (<50 watt) with the systems on and the converter not working it likely can't keep up
Check your water level and converter voltage. Post them here and we can go from there