The brown ground wire from the fan motor goes to the common ground star
under the dash, where most ground wires plug in. If you use a piece of
wire as a test jumper from the brown wire stud on the fan motor to bare
metal on the body you can test if the ground is the issue. Of course
first you should jumper the temp switch connector like Ken described,
and leave the jumper in the holes that make the relay click on. Then do
the fan motor ground jumper while the relay is activated to see if the
motor starts turning.

Mark