OK, I just tested retail unpatch Doom 3 on Windows 7 x64 and it works fine. If settings don't stick, try running it in Administrator mode? Or don't use the console and edit the DoomConfig.cfg file manually, then set it to read only.
Just waiting for the Doom 3 patch to download - were patches ever that small?
But the server is really sluggish. More info when I've testing 1.3, 1.31 and RoE too.
edit:
Tried it with patch 1.3, 1.3.1 and RoE... all work fine. I dunno what I'm doing that you're not, save editing the cfg files manually. I always prefer to do it that way...
They're all about 1.5MB PNGs, so they might take a while to load. Have to say, installing Doom 3 again made me remember just why I couldn't stand that game... way too dark and repetitive.
Anyway. If I can be of any more assistance, I will try. I don't know how much more help I can be, though.
edit 2:
Only lines I alter in DoomConfig.cfg are
r_customWidth (set to 1920)
r_customHeight (set to 1200)
r_mode (set to -1)
r_aspectRatio (set to 2)
I forgot to alter r_aspectRatio for the screenshots, but there is no difference aside from some extra horizontal - games still works at set resolution.