I've tried every one of the fixes that have been submitted for this issue, but none of them have been able to work. No other solution online has been able to get through either.
Topic on Talk:Battlefield 1942
Most of the time it is resolution/refresh rate related so I'm not sure if your case is something else entirely. Did you try running it in windowed mode? See the page for the cfg edit necessary. Also give the wrappers a shot if you haven't already.