Which is the relay for the fan?Start by verifying the fan motor itself is not the issue.
Start the car, disconnect the CTS and check for power at the fan motor connector.
If power is present verify the fans external ground is connected, if ok replace the fan motor.
If power is not present verify both power sources are present at the relay connector.
If both are present verify the cooling fan ground control circuit(relay to controller) is not open.
If all is ok replace the relay.
Yes it has a relay.Does this car have a fuse or a relay under the hood for the fan? If I unplug the temp sensor it still doesn't run.