Whenever I start a new game with HW rendering, the game crashes and I get a message saying, "Unable to compute z-lookup table." I can at least run the game in software rendering, but I was wondering if someone knows how to fix this problem?
The game also had very choppy sounds, but that problem went away when I turned off hardware sound acceleration in dxdiag.

My friend had similar problem, connected with dual-core processor. If you have multi-core as well, try running the game on one core only.
On the other hand, this sounds like something caused by GPU drivers. What graphics card do you have?

I got a Geforce 8800 GTS 512MB for my vid card. I also have a Pentium D. Do you know how to run the game with only one core?

I'm afraid I spoke too hastily. Did you read this thread?
It seems that problem with HW is well known with no ETA on fix. I'm sorry.
As for running on one core: you need to run the game, Alt-Tab to Windows, run Task Manager (Alt-Ctrl-Del), right-click on game process, pick 'Set Affinity' and uncheck other cores, leaving only 'CPU 0'.
But I don't think it will help here - my friend had older card, apparently compatible with old HW mode (Enmoku's post)

Funny enough, it is already set with only CPU 0 checked.
And yeah, I checked that other topic and couldn't find my answers. I don't really have an older video card anymore so I'm probably out of luck for HW.
Thanks, though.

You could send a mail to GOG support anyway. Maybe they would find some workaround.