The gear on the TC actuator is $20. You can test it by reversing it and see if it behaves (that will engage an unworn section). I would do that before throwing more expensive parts at it.

As Trader4 pointed out, multiple electrical problems can be a symptom of low voltage. Definitely put a volt meter on it (or unlock the cluster and use the built in voltmeter) and make sure you have 12.6V (or close) before starting it, and 13.7V (or so) with the engine running.

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David.X5
2001 X5 4.4i Sport
SOLD! at 160k miles