This happens when you're running the non-GOG CD-version without the CD in the drive. It tries to load the audio data, but can't find it so it immediately skips to the next piece of dialogue.
The immediate fix is to disable speech. This will make the text boxes stay on the screen instead of immediately vanishing.
I assume you're running the game through DOSBOX? That may be why the game can't find the CD even if it's in the drive. Inside DOSBOX, the game can usually only find the files inside its own directory.
If you really want to hear speech (you should, QFG4 has some of the best voice acting in any Sierra game), you can either do two things:
1) Install the GOG version if you have it. They worked around this problem.
2) Copy all the files in the CD's root folder (to be safe...you probably only need the resource.aud and the resource.sfx files) into the QFG4 folder on your hard drive. Then open the resource.cfg in the game folder and make sure the Aud dir and the SFX dir are set to .\ (yes, that's a period followed by a backslash)