It is useful to think of a thesis as answering a question. In your case that question would be: Are thing A and thing B related?
The setup of your thesis would then be:
You introduce the question
You than theorize why they might be related, and why they might not
You summarize previous research on thing A and thing B, and their
You describe the design of your approach (or approaches) to answer
that question, and what the advantages and disadvantages are compared
to what has been done before.
You describe the results.
You conclude by answering the question, in this case thing A and
thing B are not related.
You discuss some implications of that finding
You discuss some weaknesses of your approach and potential other
designs that might mitigate those weakness (but have other weaknesses
of their own).
It is definitely easier to write up, and especially publish, research with a positive finding. But the research is not a failure: You started with a question, and you ended up with an answer. It was not the answer you expected, but if you knew the answer before starting the research, then why do the research? So, this is not the end of your PhD.