Spasibo, Anvart!
Now we know the missing piece of the puzzle. That is why my problem went away with the installation of a new mod - the missing menu ID's from the menu_1024_768.ini file were filled in when the mod overwrote the problem menu_1024_768 file.
Pozine, given this, I would certainly follow Anvart's advice about comparing these files to see which mod changed your menu_1024_768 file and caused the problem.
A handy tool to do that and one I think is a must have is the JoneSoft Generic Mod Enabler (JSGME). See link to website below:
http://www.users.on.net/~jscones/software/products.html
JScones's great little mod is easy to use and will generate a change log to document changes to your original files. I usually just do the trial and error - run the base game check for problems, add a mod, run game, check for problems, and so on.
Let us know how this works for you, Pozine.