Well, the battery certainly isn't getting the voltage from the converter and your battery is somewhat discharged but still better than 50%. Based on that your lights shouldn't be dim, unless you are turning a lot of them on, and other things shouldn't be complaining about the low voltage.
You might want to make sure the converter is getting 120vac, and make sure there are no blown fuses or bad connections. It wouldn't hurt to check the voltage at the converter with the converter on.
If you do decide to replace the converter, buy a Progressive Dynamics instead of a WFCO.