Karen, it sounds like your batteries are dead. If you are plugged into power and your lights go dim but you have a new converter, the most likely problem is that the converter is working hard, but there is a lack of connection between the converter and the batteries.
Checking with a voltmeter on the converter output terminals will give you 13.6 volts or very close. You should have the same on the battery posts. If you don't, there is a connection problem. There are four connections, two on the batteries, and two on the converter terminal strips. Positive and negative wires between the two need to be checked and tightened.
When I had your problem, I found my negative wire from the converter to the battery on the converter terminal strip was so loose it was burning hot and I tightened it up and everything worked great after that.