This problem has been SOLVED
I was able to find a way to see the box that appears on the blank screen, the one that previously I could only hear. The box read "Compile shader material cache-this may take several minutes".
After a little more digging I found out about an official community patch, v1.75, that was not applied to GOG.com's version of Gothic 3
I was able to access this patch here:
http://forum.worldofplayers.de/forum/threads/1140053-Gothic-3-Patch-1-75-release I originally found it by another forum thread, which is here, as this person had nearly the exact same problem I did (only they had Windows 7, while I have 8):
http://www.rpgwatch.com/forums/showthread.php?t=17549 Here is information on this patch:
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After a series of non-official patches for Gothic 3, we finally present another official patch version: CP 1.75. It can be installed over every Gothic 3 version, is available for each language and contains all previous patches.
You have to start a new game after the installation. Old savegames are not compatible.
There were several changes since the last official patch (CP 1.60): Besides countless major and minor bug fixes, graphics and performance improvements, the features “Alternative Balancing” and "new A.I." were introduced with CP 1.70.
Compared to the previous patch (1.74), CP 1.75 offers widescreen support for the menus, new graphics options (like color grading and FXAA), and decreasing of stuttering by using a shader cache.
In addition, the patch includes a ModKit, the Gothic 3 Genome Lite Edition. With that ModKot it's possible to change or create new game content in limited ways. There were also more possibilities for modders included in the game. The new features and the ModKit are explained in the respective modder manual and editor guide.
Changes in that patch are listed in the changelog and further explained in the readme file.
Advices for installation:
Older Gothic 3 patches will be uninstalled automatically while installation. During that process, the backup of the file „ge3.ini“ will be deleted which was saved by previous community patches. Deletion is necessary because the patch makes important changes in the ini-files.
During the installation, modifications in the installation folder could lead to problems. Therefore please uninstall all modfications before installing CP 1.75.
Compatibilty:
Savegames of the 1.75.12 Version (Gothic Complete Edition and Gothic 3: Gold Enhanced Edition) can be used. Savegames from older versions (1.74 and older) are not compatible.
ini files of versions 1.74 or older are incompatible, too. Do not replace the ini files with older version because it could cause errors.
Modifications which were released before CP 1.75 are incompatible (except they contain only texture changes). Look into the description of a modification whether it was adjusted to CP 1.75 before you install it.
Modkit:
The installer for the modkit is in the folder „ModKit“ in the Gothic 3 installation folder. A guide will also be installed for the ModKit.
Advice for installation: It has to be installed in another folder than the Gothic 3 installation folder. Installing it in the G3 installation folder causes errors.
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I highly suggest that GOG.com add's this to their game as it increases compatibility with newer windows, as well as adding some other features and minor improvements, While it may work as it is for some machines, it doesn't work for all of them, like mine.
At the very least it should be offered as an optional download off any purchaser's game library.