Since RincewindThePissard unnecessarily closed the previous thread (Alas, poor Empire I knew thee well.) where this was being discussed (
http://www.fileforums.com/showthread.php?t=63357) , here is a new one on the subject.
It appears that I was right about changing that API call to get Doom 3 to run under Windows 98 & ME. I found this information while researching the issue. I was looking into writing a hook DLL, but this is much simpler since the unprotected Doom3.exe is available.
Open up Doom3.exe with a hex editor. Do a search for 'GlobalMemoryStatusEx'. Change the '45 78' corresponding to 'Ex' with '00 00'. Save and then run the game.
I have not tested this, but it makes sense, and the guy who posted this says he did and it works.