What's the behavior on real hardware?

What do you mean by "on real hardware"?

"On real hardware" means when you run the program without using DOSBox (i.e. on a computer that can run DOS programs).

It is distinctly possible that the game is behaving as it was programmed and that this is not a DOSBox problem.

Yeah it's not like it's a crisis to just start with a blaster when there's easy availability of weapons. It's more of a session continuing convenience, not for savescumming. DOSBox should not affect game design.

I can't try it on real hardware, because I have Windows 64-bit and I need Windows 32-bit to run it.

Then try asking someone who does have real hardware. Or asking on any of the multitudinous Jazz Jackrabbit forums out there. I would check it myself, but I don't have the relevant stuff handy.

I can tell you that despite this being a fairly well-known game, no one has ever mentioned this problem before and that it is in all likelihood not a DOSBox problem, but is just how the game was designed.

Bump. I still need help, please.

I probably shouldn't even reply to this since it doesn't seem you did anything of what was proposed above. Anyway, you're not going to get any solution to your "problem". A simple 10" google search confirms above posts and reveals that this is not a problem, the game IS designed this way. Knowing that, another 10" of proper thinking helps understanding WHY this is happening (and IMO totally makes sense).