Hi Carol and welcome back.
As far as a crankshaft, that is an internal engine component at the bottom of the engine. It is the backbone of the engine. The piston connecting rods connect to it. I attached a picture of one from a Fiat 500. It is a generic picture, but it gives you a general idea.
Based on what you said, I feel you are referring to the crankshaft position sensor. That is an ignition component and is not part of the transmission/gear box.
Regardless, if nothing happens when she turns the key, then that narrows things down quite a bit. A starter going bad, a bad starter relay, or as you mentioned, a loose or corroded battery connection or engine ground can act this way. Here are the specific links for the items I mentioned:
https://www.2carpros.com/articles/starter-not-working-repair
https://www.2carpros.com/articles/everything-goes-dead-when-engine-is-cranked
The starter relay is located under the hood in the power distribution box. Here is a link that shows how to check one:
https://www.2carpros.com/articles/how-to-check-an-electrical-relay-and-wiring-control-circuit
Now, when the vehicle fails to start, that is when you should check the starter, which is explained in the first link a listed. Here is how it works. There is always 12 volts to the bigger wire on the starter. Confirm that is present. If it is, then you need to check the smaller wire on the starter solenoid. The smaller wire should only have 12 volts when the key is in the start position. You will need a helper to test that. Regardless, if there is power to the solenoid (smaller wire) in the start position and the starter does not engage, the starter is the problem. The link is very helpful in checking it.
I wanted to thank you for your kindness and complements regarding the site. The founder, Ken, has worked really hard on making it as helpful and user friendly as he can. Honestly, when it is used by people like you, it makes it all worth the time we put into it.
Good luck and feel free to get back to me with any questions or concerns. And by the way, someday I hope to visit the UK. I have always wanted to. LOL
Take care,
Joe
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Thursday, October 11th, 2018 AT 5:01 PM