It works on both my computers; my desktop PC;
Intel(R) Core(TM) i3 CPU @3.20GHz
nVidia GTX 660 2GB
16GB Ram
Windows 7 Home Premium 64 Bits
and my laptop;
Intel(R) Core(TM) i7 CPU @2.20GHz
ATI HD6770M
6GB RAM
Windows 7 Home Premium 64 Bits
And I could write a whole composition about all the problems I had with my computers and such, but to keep it short(and helpful), here are two things I noticed;
-S IV tends to be more stable and crash CONSIDERABLY less on ATI cards. Seems like nVidia and Settlers IV don't get along too well,
-Right out the box, I only had the 3D graphics problem(on these two computers) with a german vanilla Settlers IV copy(none other version has given me this problem. And I've installed like 4 or 5 different versions). I know that you're probably playing the GOG release(which didn't give any problems in my case), but I thought I would just tell you, in case it SOMEHOW helps.
Anyway, best of lucks with getting your game running! :)