This is the wire going into the front axle

Thats the 4 pin i disconnected after discovering the broken wire

I got a 1990 chevy 1500. My 4x4 doesn't engage. I thought it was my actuator. But when I crawled underneath I found a white 4 pin square connector going into the front axle with a broken wire. What is this wire for and would it cause my 4x4 not to engage.

 

I assume the wires from that plug run to the location in your top pic. That is the switch that kicks on the 4x4 light when engaged.