As stated in my previous thread; I had been encountering an issue which would prevent me from playing VTMB without using the -dxlevel 80 parameter in the command line. This would allow the game to run, however textures from any object that wasn't a floor, wall, ceiling, or door would render so dark they'd almost appear black.
Scouring the internet while simultaneously seeking help here, I discovered two important things; the Intel G31/G33 graphics chipset isn't among Intel's list of compatible games (despite much more graphically advanced games' presence), and almost every thread on every forum I found, nearly everyone who's copy of VTMB would crash on startup also had Intel G31 or G33 graphics cards.
I was never able to determine the source of the incompatibility, but I did find a solution.
3D Analyze is a powerful tool that tricks your games into thinking your graphics card is something it's not. According to various sources (most reliably, the GameSpy Network forums), the best version of 3D Analyze to use with this particular issue is version 2.26.
Once you've installed the tool, your setup should appear as such:

Obviously, steps 1. and 2. should match your own VTMB install directory.
If you want to play with the console enabled, create a batch file for 3D Analyze to run:
1. Create a new text file in the same directory as vampire.exe
2. In the text file, type "X:\vampire.exe -console," where "X" is your specific install path (default is "C:\Program Files\Activision\Vampire - Bloodlines")
3. Save the file as "vampire.bat"
4. Keep everything else in the above image the same, but click the "Select" button for step 1., switch "Executables" to "Batch Files," and select your newly made vampire.bat
5. Launch the game and enjoy your console!