Several attempts to remove and install the geck were unsuccessful. A system error stating "The program can't start because libvorbisfile.dll is missing".

That has nothing to do with Windows 7. You are installing the geck to the wrong place. Make sure to install it into the same folder containing Fallout3.exe. It should be "BethesdaSoftworks\Fallout3".

I'm pretty sure Gunmaster95 is right I have windows 7 and the G.E.C.K. works just fine for me.