All the above, plus the relay, plus the dashboard switch are possible causes. Best to investigate carefully before buying parts.
1. check purple wire, as stated.
2. check voltage at motor (at purple wire) if it has voltage (4 - 12 v depending on setting) WITH THE WIRE CONNECTED TO THE MOTOR then replace fan motor.
3. if no voltage at motor on any setting, check fuse.
3a. if no voltage except on high, check resistors
3b. if no voltage only when on 'high' check relay
3c. if no or low voltage at motor when connected, but 12v when purple wire is diconnected from motor, see bottom paragraph.
4. if fuse is OK, check voltage at relay input and output. Re-seat relay and re-test. Probe relay voltage from back of socket with relay in place. If low/no voltage, check dashboard switch.
FWIW: when mine went out, it turned out to be the switch at the dashboard. It was a pain to troubleshoot, because voltages all looked OK with NO LOAD (relay pulled out, probing the contacts in the socket). When I finally tested with relay in place, I found low voltage. The little PCB in the switch was burned. I now have a spare blower motor

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