I downloaded demos for this game from Filefront, Gamershell, and none work in my Windows Vista 64 bit. Just trying to install it normally says "OS not supported". Running as admin *and* telling Windows to use the "recommended config" will install the game successfully, but the game itself doesn't run.
So does someone know where I can find a version for Windows Vista 64 bits? GOG? Anyone?

This seems to be the only one for Republic. Or the official one at least. Have you tried changing the properties of the game's .EXE to a different compatibility mode? Such as "Windows XP" this might trick it to work.

I tried this and this is working for me on Windows 7 64 Bit RC.
http://www.bigdownload.com/games/republic-the-revolution/pc/republic-the-revolution-demo
I turned XP compabilty on BTW.

Both of these files worked at work, on a Windows Vista 32bit machine, and both didn't work on Windows Vista 64... running it as admin, compatibility mode, tried different settings, downloaded from different places... no deal! I might be really out of luck here.
If anyone out there did play a Republic demo on a Vista 64, let me know how you pulled it out please.