Sounds like time to start the education on Rv as it is a pretty steady diet!
We all keep learning new things!
One of the big thing on an RV is learning what makes the electrical stuff work,
so time for some basics!
Not meaning to talk down to you if lots of it are things you know but easier /quicker to mention it all on start than to skip too much and leave you in the dark! Sorry about any unintended insults!
When you plug into power it sends 110volt Ac power to a converter lots of times that converter is built into the back of what we call a load center. The load center is a big deal to know about as it does lots of things for different parts of the RV.
One big thing is to know where the load center and converter are! There is likley to be a cover with lots of breakers and fuses in the Rv. That is the load center and if the converter is behind it, there will often be a hum when plugged into power as well as a fan which runs when the converter gets warm.
Inside the cover there are often breakers or fuses and many times they are labeled.
Some are to protect things like the wiring to the Air conditioner, normal 110AC outlets, and microwave that use 110 Ac for power.
Often under the same cover is the group of fuses that provide protection for 12 volt DC things. Those are often the little plugin fuses for the inside lights, vent fans and controls for some of the 110AC thing like the furnace and thermostat that works it and the Air conditioner.
Looking it over and knowing where to look for a blown fuse or breaker tripped is one way to feel better and recover quicker if you do have trouble later! It's easier to learn what makes what work if you are doing it when you can see it work! Pull a fuse out of the circuit for lights and at least some of the lights will go out until you put the fuse back!
Understanding what will work when plugged in but the batteries are not working is not that hard in many cases.
I did a little shaky drawing to help!
Click this snip to see it better!
Power from the cord comes into the load center and converter on back as 110AC. Some goes directly to the breakers or fuses for AC power and out to microwave Air conditioner, and outlets.
But some of that AC power also goes to the converter which uses it to "make" DC power!
Some of that DC power goes to fuses which feed lots of stuff like lights, fans and controls for heat and AIR.
BUT the part you are asking is the way the batteries help or hurt! There is a connection from the 12VDC out of the converter which connects to the batteries. Think of batteries as simple storage like a pantry! It's where you put extra when you have more than needed but also where we can get what we need if we have none coming in from the outside! The blue line shows this as a two way street, it goes into or out of the batteries as needed!
This is kind of sketchy and may miss lots of small points on how and where things connect but the general idea is the same on all Rv I've seen!
If the power cord is NOT connected, we expect to use the stored power in the batteries. But yours may not work!
So when plugged into power We use the AC for Air cond and microwave and expect the 12VDC things to work off what the converter is making, so not a lot of loss of function!
The bad part is that we are not going to store any for later when we unplug!
If a shop has the drawings and any idea of what they are doing, they should easily be able to find and fix this in 3-4 hours as it is not that big a deal!
If they know where the converter is and it is working, they should be able to tell if power is getting from there to the batteries!
If they know where the batteries are and where things like the lights are, they should be able to see power gets from one point to the other!
It's not like they have a hundred feet to lose it while looking!
One thing they may not know about is the bunch of fuses or breakers under the front frame of the trailer in many cases! It's been a pretty common source of problems on the forum if that is the problem as folks who never worked on a trailer DO have trouble spotting a tiny little breaker inside a metal box there! But the reason you took it to a shop is because they are supposed to know about those things!
Maybe they need to call Winnebago and ask for help? That's what lots of folks here have to do when we run out of good ideas!
I hope that helps some and know that the group is with you and wishing life was different!