Here's what I did:
1) Downloaded hi-res patch from here http://hrp.duke4.net/download.php
2) Extracted the files from "eduke32_win32_20121220-3308" to my game folder (in this case: C:Games/GOG/Duke Nukem 3D)
3) Run eduke32.exe and chose the settings to match my laptop res
4) Launched the game in eduke32 by selecting Start
My laptop runs Win 7 x 64 and I don't think it's relevant but I have a NVIDIA graphics card (I think it's a GT420). I'm also running the eduke32 as an administrator.
Any help or suggestions would be much appreciated. Thanks.