BloodCloak: Had this problem too. Just solved it by replacing the 'atiumdag.dll' with this one:
http://www.mediafire.com/?wzm379223amren2 Looking at the default one included in the populous folder it is dated at 2009. I'm guessing it doesn't have references for newer cards? Anyway, this one seems to work.
Details.. after changing that .dll file...
-double click the D3DPopTB.exe file
-main screen is fine at first, but
-when I exit Tutorial mode, the menu screen is all "rainbow and psychedelic"
-gameplay screen is fine thus far, maxing out at 800x600
All of the previous suggestions below haven't worked...
-reinstalling the game
I did so through the installer, of which that was DL-ed via the GOG downloader program/app
-RC compatibility on the shortcuts and changing them to win98, win95, winXP SP2, and winXP SP3
-changing the shortcuts to point to "<path where Pop3 is installed>\D3DPopTB.exe"
I'm on Win7 Home Premium with SP1
AMD Radeon 6600