"The terms of my lesson agreement are that if I cancel the lesson with less than 24 hours' notice there is no charge for the lesson. If the student cancels it with less than 24 hours' notice, I charge the full fee."
"I turned up for the one hour lesson on time and waited, no reply. They didn't show up. After a bit, I get a message from the parents to say there is no internet access for the student so no lesson."
There are several factors to be considered.
Whether you state it or not, whether you cancel with 1 minute's notice or with 1 month's notice, it is not that "there is no charge", it is that you will obviously not get paid.
You want to have the freedom to cancel whenever you have to, without any penalty, but you expect to be paid if the student has to cancel. That is one sided flexibility.
You didn't turn up anywhere - you started an online tuition session on your computer in the comfort of your home.
If you had a problem with internet access, you would have done exactly the same thing as the parent did. Or would you have offered to pay them compensation?
The customer is always King, especially if you want the custom, which you do.
If you had agreed to regular tutoring, a fair way would be an understanding that if either party has to cancel, the session should be rescheduled.
If after a few sessions, you feel that it is not working as expected, you stop tutoring the student.
Generally, tutors are in demand and can lay down the law.
But I believe in a fair and flexible approach, knowing that one is dealing with school students who can have all sorts of reasons to cancel, including last minute. The goodwill of parents and students to this approach more than makes up for it.