Now that I finally have Populous 3 again and they've done all this work to get it to work on modern Windows systems (works great on Windows 10 btw), I want to run it on my retro PC with my CRT monitor. It runs on Windows XP. But it refuses to run any of the 4 .exe files in the folder, simply displaying an error popup. "The application failed to initialise properly." followed by an error code.

Searching this messages suggests the game can't find certain DLLs, but I have no idea which ones XP would want.

Are you trying the Direct3D ones, or the Software Mode ones?

There were 4 exes and they all gave the same error. D3DPopTB.exe, D3DPopTBW.exe, popTB.exe, and popTBUW.exe

Okay, that's a little strange. One of those sets, should work.

Do you have directx 9.0c redistributable installed?
On your xp machine.

A bit late to the party, if you still have problems reply to this comment or drop me a Personal Message and I'll have a look.
I have a few old laptops with XP but there's no point in digging them if you already fix the issue.