Well it worked for me when I did the same thing just recently.
This is what I used to have it work -> [
www.grandprixgames.org]
One file is a patch, and other is a decrypt EXE. I patched my GP3 first, then replaced the EXE. All worked and I could modificate my GP3.
Maybe try reinstalling Grand Prix 3 or at least reinstalling the patch. I suppose you can remove it from programs list in control panel, but try removing it from Regedit before installing again. But maybe you don't even have to do that, from your latest post it just seems like you posses a wrong EXE.
And use the link provided in this post to do the whole thing or just for the no-cd EXE. I hope you'll succeed!