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Since you have power at the pink/white wire of the blower motor the relay and mode switch are good. The resistor should not have power. The motor gets a ground from the switch/resistor. If the blower works just on high speed then it is a faulty resistor. If it will not work on any speed then I suspect a faulty switch. Go to that resistor and you should have a ground at the black wire. Then you should have ground at the yeloow/red on third setting, and on the light green/white when on second speed setting.
Are you saying to pull the connector off the resistor and check for the ground on the connector wires with the different settings?
okay, I am getting ground on black, orange and yellow when the selector switch is on max. I get ground only on black on all other selector positions. The orange/black wire on the fan blower does have a good ground with everything on.