Is it my battery or converter

I am having electrical trouble with my 1998 2518. We just bought it used last October and didn't even have time to use it last season. I opened it up yesterday to air it out and start spring cleaning.

I neglected to disconnect the battery over the winter. There is a deep-cycle marine battery (12V) attached. I put the battery on a portable charger for several hours. It reads 11.88V with a digital multi-meter. However, I get no power on DC in the trailer.

I checked the battery cells and topped off a couple of cells and I plugged the TM into shore power overnight. I hear the converter humming when it is on shore power but it doesn't appear to be charging the battery.

How can I troubleshoot this further? It appears to me that if the battery is reading close to 12V, it should be able to at least power a light bulb inside??

Thanks for any help and look forward to camping this year!

Dean

Lancaster, PA