Not sure if this would be better posted elsewhere?
I have had quite a few problems getting DK2 to run after transitioning from windows 7 to 8. One of those is that after alt+tabbing out and back into a game, the screen would go black but the sound would still play. Indeed, i was able to deduce that the keys still respond by pausing and unpausing the game, noticing that the sounds of the imps footsteps would stop and resume.
If your playing on a laptop with an integrated and additional graphics card (as i was) and are still suffering problems after trying other solutions, try setting the game to run on your non-integrated graphics card.
This can be done (at least for me) by right clicking on the exectutable and going to run with graphics processor then selecting the appropriate option.
I'm honestly annoyed that i didn't think of this sooner, espescially since i have used this fix before on more recent games.