I finally got it working (Thanks DDHack), but I'm stuck on the copyright screen because it's not accepting any input from my keyboard. Anyone else have this problem or a fix? Thanks in advance.

EDIT: I know it's not my keyboard bc I can Alt+Tab out of it.

Have you got any kind of gamepad, joystick or similar input devices plugged in? Remove all but mouse and keyboard.

If this doesn't work, try disabling the game's gamepad support in the registry (as you can't access the in-game options menu)
Open the system registry (Run => regedt32) under HKEY_USERS find Oddworld/Munch's Oddysee/Config and edit the JoystickIsOn setting and change to 0 (zero)

Well, this is interesting. It started freezing my computer again. Keep in mind, DDHack is installed. WTF game? WTF?

DDHack should only affect graphics as it is a wrapper for the old DirectDraw library. If the developers used DirectX for controls then it's done with DirectInput library. I don't know how DDHack is implemented but it's not supposed to interfere with DirectInput, well at least it shouldn't.

Btw, which Oddworld title are we talking about exactly?

Doesn't matter. I figured it out. Turns out my graphics driver was incredibly outdated. Thanks for the help, though.