I've started playing the version of Police Quest 2 from GOG, and have encountered two minor but very annoying problems:

1) The introduction sequence moves WAY too fast.

2) The display is "squished" (there's about an inch of black space between the top of gamescreen--the status bar--and the uppermost edge of my monitor's display)

I am playing this using the desktop shortcuts and version of DosBox provided by GOG.com.

Any help anyone can offer would be greatly appreciated. Thank you.

Which sequence are you referring?

He probably means the opening sequence. I've got that problem too. The music is fine though, just the video.

It's definitely more playable with ScummVM.

I recommended it just in case of a DOSBox error. ScummVM is designed to not have any errors at all.

Okay, well, I solved the problem...sort of.

The title sequence runs at the proper speed (and the game display fills the screen), IF I open DosBox itself and start the game from there. I don't know why that method works while opening it via the Desktop Shortcut causes it to go turbo speed, but that's the what I've discovered.

I was able to fix the super-fast opening credits by doing the following:
Go to C:\Program Files\GOG.com\Police Quest 1-2-3-4\Police Quest 2
Find a configuration file called "dosboxPQ2" and open it. Notepad will pop up with the config options.
Scroll down until you find a section labeled [cpu]. Below that you should find some options that look like this:

core=auto
cycles=max
cycleup=500
cycledown=20

In the option "cycles", change the value (the item on the right side of the = sign) to auto. It should now read:

core=auto
cycles=auto
etc...

That fixed the opening cutscene playing too fast for me. Hopefully it should work properly for anyone else having this problem.