11.4 with 13.4 at battery is too much voltage drop.
I would start at the battery, clean both the negative and positive connections.
Next Trace the negative to where it makes contact with the frame. Clean this good and apply some electrical grease.
Look under the frame near the connection of the TV umbilical cord for a connection that could be either a fuse or circuit breaker. Insure that these connections are clean and tight.
Look on the frame in the vicinity of the converter for the negative connection. Clean and coat this connection.