I am using LimeSurvey Version 1.92+ Build 120330, which could be my problem.
Yes, this might be our problem. Your software is almost (missing 15 days) 7 years old! In web application years this are decades. So I would highly recommend that you do an upgrade to the latest version, or at least to 2.6.x, but the fork from the very same Denis Chenu, who is still supporting a branch of LS that is 2 major versions behind, for free.
github.com/SondagesPro/LimeSurvey-SondagesPro
If you look at his Github you'll see an impressive set of plugins he created and provides them to the community for free:
github.com/SondagesPro/
You should really consider do at least this upgrade, if you don't want to move to LS 3.x, because your installation hasn't received any bug fixes for 7 years now. So as a client, I wouldn't allow to collect data on such an old installation.
Now to you problem: I don't think that question / group relevance existed back then, I think it made it into LS only with the 2.05 version, but I am not sure anymore, this was so many years ago.
What you could do is to use conditions instead. It is a little bit more work in my opinion, but conditions should have existed.
What you do is, you create a first question like Joffm suggested, where participants make their choice.
Then, based on this choice, you set conditions on the questions / question groups that you want them to see and the ones you want to hide.
However, all this can be done a lot easier and quicker with question or better group relevance, so you might want to install either 3.0 or the fork from Denis if you have custom themes (they won't work in 3.x).
Then have a look at how far LS has come from 1.92 to even the 2.05/2.6 branch.
Unfortuantely (or better fortunately) I don't have such an old installation (and I doubt anyone else here does) to be able to check what is possible in 1.92 and what is not.