Why are half my Christmas lights not turning on?
On Christmas lights, they are wired with a backbone of 2 wires carrying power through to the socket on the other end. 

Then, they have one or more strings of 40-50.  Each string taps one backbone wire at one end, and the other backbone wire at the other end. 

Within each string, all lamps are in series.  A failure will darken the whole string, except the bulbs have fusible shunts so if a bulb burns out, it will shunt and the other bulbs will remain lit (at a slightly higher voltage, burning them out faster). 

When you have a segment with 40-50 out, that means a shunt has failed, or you have a loose socket or broken wire.  

They make toners specifically for Christmas tree lights (a cheapie version of a Fluke toner, I presume) that will help you find the bad one.