I know the game from old MS-DOS days, since I am here I looked into this topic.
Wish I had the solution at hand immediately, I do not. But now I remember I had the same issue even on my old MS-DOS machine. Back then a 486 DX 33 Mhz. That was 20 years ago, so don't insist on me remembering how I fixed it in detail. So the first good news I can give you: the issue is not with the game, it's the machine, in both your cases a virtual one, but still solvable as I solved it back then.
GoG releases should work out of the box, but they do not always. This is no criticism. It happens. I also had issues with getting Theme Park to run at playable speed but solved that.
Back on my machine it was a settings issue... config.sys and autoexec.bat always needed some fine tuning to provide the memory necessary to play for this or that game. The second issue you often encountered was graphics related, remember Univbe drivers for SVGA? If the driver was the right one, all was fine, if not you encountered crashes, sometimes with error messages pointing to something else, but in the end it indeed was an Univbe issue.
Key pressed on keyboard and beeps usually mean bad fitting keyboard in DOS. You can't do anything about that, I know, impossible to unplug. But technically it could be some other Windows task causing the issue. Actually just yesterday when I played Batman Arkham City - I usually tend to Alt-Tab out of the game to do other things - suddenly when I was back in the game and presssed the spacebar I got a beep and return to desktop... Something went screwy. Normally everything worked fine, and did so again after I rebooted the system.
I know for sure the game not going further issue, is caused by something like I stated above. Either some memory settings are wrong, or it's the graphics and when the game is supposed to load further data it simply can't do so and you're stuck. This also applies to graphics even if you play the game in VGA all the time.
Issue remains even when playing in fullscreen mode?
Maybe the issue is a DOSBox settings override from another game?
Have you closed Windows' Explorer.exe before launching the game?
(This often helps with some games, can restart Explorer.exe after you exit the game by: Start-Key + R (Run dialog) and then typing Explorer.exe there.)
Can't give you more help, since I'd have to see your DosBox config files and settings. Anyway, take it from me, it is solvable.
