Looking at mine there are three strings of black/white G.I. lighting on the back box board. You'll just need a voltmeter and a few minutes. There are several connectors stapled to the back of the board and the backs of the sockets to check for voltage. G.I. lighting is 5 ish volts AC, so measure from black to white in each connection and bulb base, starting in the line from the bottom right (as viewed from the back) and you will find your problem right around wherever the voltage disappears.
When I got my LW3 the G.I. lighting was not happy, the connector to the board was burned, half melted, but amazingly still working. My suggestion no matter where your problem ends up being is to replace the connector plug in the back box. The connector and the little plastic tool to set the wires without even stripping them only costs a couple bucks online, much cheaper than clean up after a fire if they look heat damaged at all. I also went through and changed out many of the 44s bulbs with 47s that draw less current.