So I've spent the last two days trying multiple patches/fixes to get Jedi Knight to play with the 3D Acceleration on and none of them have worked. They either get the screen to show up without the HUD, or they outright crash the executable. I have no idea what I'm doing since I've never really had to do something like this before, and clearly the patches work, otherwise there wouldn't be multiple threads on here recommending them.

I really, really want to have the chance to finish Jedi Knight (and, by extension, MOTS) since I've never done it before, so any help on getting the thing to run smoothly would be greatly appreciated.

My specs-
OS: Windows 8.1 64bit
CPU: Intel Core i7-4700MQ 2.40-3.40ghz
Intergrated GPU: Intel HD Graphics 4600
GPU: GeForce GTX 765M 2GB
Ram: 16GB DDR3

PS: It's an Alienware 14 laptop, so maybe that's hampering my efforts somehow? I dunno.

I had the same problem with Dark Forces 2. I finally gave up and tried the integrated GPU, which ran fine. Perhaps you can switch to your Intel HD Graphics while playing DF2.

Interestingly, MotS did run with my graphics card, after applying one of the patches/mods. Unfortunately I do not remember which one it was.

Funny thing is, that's already the default GPU JK is using when I launch it, so I have no idea why it's not working. Maybe I should flip it to the Nvidia card?

EDIT: Nope, that didn't work. Get the same thing running the GOG executable with either GPU: black screen with only the HUD showing up.

I can replicate that black screen problem with my ATI R9 285 using the latest Crimson drivers (Nov 30th)

Have you tried using dgVoodoo2?

http://dege.freeweb.hu/dgVoodoo2.html

Download dgVoodoo v2.45
Extract archive
Copy:

DDraw.dll
D3DImm.dll
dgVoodooSetup.exe

Into the root game folder i.e:
C:\GOG Games\Star Wars Jedi Knight - Dark Forces 2
C:\GOG Games\Star Wars Jedi Knight - Mysteries of the Sith

You should be able to enable 3D acceleration through the in-game menus and enable 1080p, etc.

Fixes it for me - but there is a slight delay at the very start of each level.

Windows 8+ has issues with older Direct3D games. It's not about the GPU you're using, but a DirectX library.

Alternatives include downgrading to W7 (Intel HD 4600 ran fine on it), installing dgVoodoo2 (as mwnn has said; it worked for me on a modern W10 laptop, both with Intel and Nvidia cards), or installing one of the unofficial patches around (haven't tried any, though).