[Tom Wesenberg]

I'd say it's the inverter, unless you have a switch to remove power to it. I didn't read where you disconnected the inverter and checked for draw. I hope you are using an analog meter, and with an unknow amp draw or voltage reading, always start the meter on the highest setting and work you way down. Depending on the size of your inverter, you could have from milliamps to an amp or more draw, even with no load on it.