If you have a multimeter check across the battery terminals which should read 13.6VDC when you have shore power on and 12.6VDC if the shore power is off and the battery is charged. If you dont have a multimeter then you should go get one. They are very inexpensive and can be purchased at LOWES, WALMART, any number of auto parts stores for $10-$20. Everyone should have one of these in your RV TOOLBOX... Looks like this
While you are at the battery terminals you need to confirm the battery is hooked up correctly. This is real easy to get reversed.
What I do is look on the battery case and find the word "NEG" or the symbol "-" and make sure this connected battery cable goes directly to the TRAILER FRAME GROUND which should be real close to the battery.
If this is reversed then you will find a blown 30AMP in-line fuse real close to the battery and also two fuses on the 12VDC DC POWER DISTRIBUTION PANEL (where all of your 12VDC fuses are located) labeled "REVERSE POLARITY"...
Change the battery cable to their correct terminals and then replace the blown fuses.
Let everyone know what you find out...