Once you've installed Team-SiMPLE's normal fixed BF1942.EXE (Step 8 in the
http://ea117.com/dcinstall instructions), the graphic resolutions offered inside the game should be "exactly the graphic resolutions offered by your video card." Rather than the fixed hard-coded list of 800x600, 1024x768, etc., that the game otherwise offers.
Have you installed that updated BF1942.EXE? If not, I would try installing that and see how much of the problem remains. If the problem continues even with the updated BF1942.EXE, or you already have it installed, what graphic resolution is currently selected in-game? Is it the same as the desktop resolution your new PC normally runs Windows at? e.g. Both the Windows desktop and the game are running at 1920x1080 or similar.
Other discussion:
There are certainly a lot of folks who report "getting a black screen" as one of the problems they have had with Battlefield 1942. Such as
this discussion here on Team-SiMPLE, although I personally
would not attempt using any of the solutions attempted by the original poster in that thread. i.e. The BF1942CF.EXE and the Wine3D package. Neither of these should be required for successfully playing on Windows 10; nor can I vouch for how "safe" BF1942CF.EXE is, whatever that is.
What I
do think has merit in that thread
is the information in the post by NUKE, about how switching the game resolution to 800x600 made his behavior go away. And then by manually editing the BF1942.EXE binary file
as recommended by Team-SiMPLE's tuia on bfmods.com, to eliminate
"BF1942.exe is hardcoded to start at 800x600 and after it reads values from game.setGameDisplayMode", such that he could run his actual preferred resolution again.
Meaning instead of the code currently in BF1942.EXE that tries to always run at 800x600, they modify the BF1942.EXE to default to whatever screen resolution the player actually intends to normally play at. So that the game isn't switching back and forth between 800x600 and some other resolution, on the premise that in some machines this switching leads to the "black screen" issue. That chosen resolution is of course different for each user, which is why the change has to be customized, and isn't just a "here, it's fixed" kind of change that can be provided.
Note that not just on Team-SiMPLE, but in many places I've seen folks recommend that you need to
set every Battlefield 1942-related process to XP compatibility mode and Run as Administrator. Personally, I've only ever set BF1942.EXE itself to XP compatibility & Run as Administrator, and even that is automatically done by tuia's BF1942.EXE patch. (Step 8 in the
http://ea117.com/dcinstall instructions.) Note that in the BFMods.com post cited above, tuia also indicated that programs like Blackscreen.exe aren't even being used any more after the latest Battlefield 1942 1.61 patches. So I really don't think "set all programs including Blackscreen.exe to XP compatibility" is really the answer, either.