Hey everyone,
I was having a similar issue to the sounds of this one and I managed to find a solution to get my game working. I don't know if you guys had the same problem that my PC did or if this solution would work for you, but I thought it worth sharing just in case.
My issue was that I would access BF2042 through either Steam, the EA app or through opening it up directly via the Windows Start Menu. The initial screen would boot up featuring the BF2042 intro screen and the Easy Anti-Cheat bar, after which it would transition to a collapsed black screen but would shut right off shortly thereafter. No warning, no error, just shut off. If I accessed Steam to try again, this process would repeat over and over. That was my problem.
The solution that fixed it was rather simple. I just checked for the game's file integrity using Steam. This YouTube video shows how it's done (starting at the 2:06 mark) https://youtu.be/RM4py6-dF8Q?t=126 Once I ran the process, Steam said it found some issues with the game's files on my PC (and apparently, it had rectified them too, I guess). After consideration, it was clear my actions had been the fault in all this. For other reasons, I had deleted then reinstalled BF2042 to fix a separate issue and I think with me restoring some old files from the recycle bin, deleting some I thought were unnecessary duplicates, yada yada yada, the game never installed correctly in the first place. But using steam to check out the game's integrity managed to restore the whole thing to working order.
I didn't do anything beyond that - it was just this one action. Like I said, it might not be enough for you guys whose problems could potentially be more serious than this, but I still thought it'd be worth mentioning. Regardless, I hope you guys have luck fixing your situations.