Can a thesis not answer the research question and still be good?
The short answer to your question is yes, you can have a good result even if you don't (completely) answer the original question. However, the advice you really need is from your professor. Don't express negative feelings about how he "forced" you or anything like that. Ask him for his analysis of your work and how to best position it. 

Many research questions take a long time to resolve. Don't be discouraged by that. 

But the work isn't a failure, and you, especially, shouldn't think of it that way. You want to ask yourself, however, "What, exactly, did I demonstrate in this work". Your wording of the rest should revolve around answering that question and showing how you did a good job of it. 

You can have a final section that discusses how this work is part of a larger work and briefly describe the problem you started out to solve. 

However, some of your statements confuse me. You seem to be saying that at some earlier point you gave a title to the university that makes a claim of success to the earlier question, and that that can't be revised. Such a policy would surprise me and I would make doubly certain that you are correct. But advice from your professor would also be valuable here. 

When it comes time to publish your work, there is no rule anywhere that I know of that restricts you in the title of the paper(s) that get produced. So even if you are sort of "stuck" with an inappropriate title, you can just treat it long term as an anomaly. You then have a little joke you can share with future students if you stay in academia.