On initial start, you see an "Text: Invalid videomode specified" error before or after the initial splash screen.
You're probably running at 16 bit color.
Battlefield 1942 starts at a default 800x600@32, or 32 bit color and requires this for the first run under Wine. After you get into the GUI menus, you can edit the video resolution to your liking such as using 16 bit color. Make sure your /etc/X11/xorg.conf file matches the bit depth.
(On a side not, I'm not sure if it's required to have the 800x600 resolution or other resolutions also listed within the xorg.conf)