I don't think that the dom install touches the windows registry at all. It basically just creates a folder and plops the game files in it...
Ah.
I renamed my original dom3 directory and did a fresh install.
Vista is your problem. (Have I mentioned anywhere that I HATE VISTA?)
I created a new game with the new install and low and behold, no saved games folder appeared in my new dominions3 directory.
I named the game StupidVista and then clicked through a hundred buttons to make vista search the entire hard drive and not just the "indexed" locations (thank you very much MS...) and found the game here:
C:\Users\Ballbarian\AppData\Local\VirtualStore\Pro gram Files\dominions3\savedgames
Well of course! Why didn't I think to look there in the first place.
Probably the easiest solution to your troubles would be to just copy the game folder back from your old PC again and put it in a location that makes sense to you.
Mine is in:
C:\Games\dominions3
Then just make your own shortcut by right clicking on the dom3.exe and put it on your desktop, or in your start menu.
Hope this helps.