The shuttle taxi I ordered didn’t come and I couldn’t get in contact with them, so I got another taxi. Now they won’t refund the money I had paid.

If you were waiting at the agreed-upon location at the agreed-upon time and the taxi didn’t come, plus you couldn’t contact them, then you should be able to get your money back, so confirm the reason why they would not issue a refund. Sometimes a shuttle taxi is included in a travel contract, so check the terms of the contract, then talk with the travel agency that runs the tour.