Thanks for letting us know the outcome. I am glad that you have been able to settle this out of court and they are willing to accept this payment and issue a final warning.
In terms of the TVM being out of order at the station boarding. Taking a picture is a good idea. Using the help point at the staiton is also a good idea as you can speak to a reaal person and make a note of their name. Also you don't need to do this but if you wanted, you could phone the customer relations of the TOC that runs the station and ask them for permission to travel. I've never done this personally but it is a reasonable phone call. Again, you could get the name of the person you spoke to and ask them to log your call. It might also speed them up in terms of fixing it if they see customers are calling in about the matter.
However, as soon as you get on the train, approach the guard (you will see what part of the train he/she is at when they operate the doors at the staiton) and say the TVM is out of order and you wish to buy a ticket.
My understanding is that when they go out of order it is logged so the staff on the gateline at Crewe would be able to check this.