I answered my own question. There is a bug in the version of this game as posted on this site.
It has to do with the sound card of all things. I followed this link which another submitter already has posted:
http://vogons.zetafleet.com/viewtopic.php?...38e313c3d3bc875
And I followed its instructions. It requires you to locate an uncracked version of this game. They mention where you can find it, but do not specifically link to it, nor will I.
You need to use the following command to mount the folder with the game installer as a floppy disk within dosbox.
mount a <path to directory> -t floppy
mount c c:\dosbox
Note: instead of c:\dosbox you can use whatever directory you want.
Then you run the install.exe from the A: drive, and install the game using the PC Speaker rather than soundblaster audio. You also have to use the EMS/XMS option for graphics. The problem with the cracked version of this game is that it is set up for soundblaster audio, and DOSbox doesn't do well with that apparently.
You do still need the original LD2.exe from this site, however, as it has cracked the copy protection. Just replace that one file after installing the game and you'll be all set. Mine is working perfectly now.
I can drill suture holes just fine...although I havne't successfully completed the operation yet...I forgot to induce hypotension before I manhandled the brain...doh. Oh well, it works now, and the audio is MUCH better.