I have a little bit of an issue with the sound. Actually, it's kinda a big issue in the long run. I guess you can say that whenever a major cutscene plays, about halfway through, the sound just goes off completely, and the sound isn't restored until the gameplay is back.
Anyone else familiar with this issue? If so, you know how to solve it possibly?

Back up the original gog dosbox config and try changing these variables in the config. Verify proper audio functionality before going into full screen.
[sdl]
output= overlay
fullresolution=0x0
windowresolution= 800x600
fullscreen= false
autolock= true
[dosbox]
machine= vga
[render]
aspect=true
scaler= normal2x
[cpu]
core= normal
cycles= 10000

Is there an easier way? How do you backup the original dosbox config?

To backup the original dosbox config file, just copy it to another location like your desktop or 'my documents'. If you ever need to restore that file, just copy it back to its original location, in the game folder

I don't have the GOG version as of yet so I'm basing this off how I got my retail version working using dosbox. I'm kind of assuming they used the dosbox version. You should see a dosbox splash screen if it uses it. Or you can check in the game's install folder and see if you see a folder called "dosbox" in there.
Before you do this make sure you have "hide extensions for known file types" deselected in the "folder options" under the "view tab" so windows can display the file extension. (see attached pic)
Their naming convention for the dosbox configs is usually dosbox<game name> (without the carrots) with a .conf file extension. Once you find this you can just right click on it to copy it and back it up somewhere. Next you just open it in a text editor like notepad and scroll to the main sections listed (sdl, dosbox, renderer, and cpu) and make the following changes. If it's difficult to find those main sections use the search feature in the text editor (notepad.exe).
Out of curiosity, what is the "date modified" time stamp on the file named "DACBLAST.DRV" in the main game folder?
You can right click on it and select properties on it to find out. The reason I ask is that file is a soundblaster driver used with sound. There were some patched versions of that driver floating around that made the sound work better.

Date Modified: Wednesday, August 16, 1995, 11:51:00 AM
I looked in the dosbox folder and there are no files marked .conf They are mostly .txt Although if I click on the dosbox .exe and then type "dir" in that window, there is a config listed in the directory. Though it doesn't do much when I type "config"...

The file you're looking for it's called 'dosboxPHANT.conf', except it's not in the DOSBOX folder, it's in the game folder.

Ok! Everything is working now. Thanks a lot!

No problem ;)

Glad to hear it's working. Since it works fine now you can try to increase the quality of the "scaler" in the "render" section to help smooth out pixelation. If the sound issue comes back you can just drop it back down to "normal2x"
Example of a better quality scaler :

[render]
scaler=advmame3x