Same thing happened to me yesterday. I didn't do anything with the computer, no new installation, no new updates for days. All other games worked fine (Need for Speed, BF4, first Battlefront), but BF2 would not launch - it always appeared for about 5 seconds in Task Manager and then disappeared - the game window would not appear. Origin show I was playing the game for few seconds, then return to being online out of the game. Windows Event log registered no problem, no failure anywhere. Windows acted as if I launched the game, then quit it and evering was fine. I tried EVERYTHING to fix this and nothing worked. I tried Origin update. I tried Origin repair. I tried deleting game exe files and Origin Repair. I tried deleting game Documents folder with settings. I tried removing all Origin folders from AppData and ProgramData folders. I tried Origin reinstallation. I tried game reinstallation (freaking 64GB again took me 18 hours to download!). During the game download I could start the game and play Arcade tutorial, but once the download finished the game would not start again. I tried running the PC in diagnostic mode. I tried running a restore point to return system few days back. I tried reinstalling Visual C++ 2013 Redistributable packages both x86 and x64. I tried updating Windows (no updates available). I tried updating nVidia drivers. I tried to run the game as administrator. I tried launching the game in offline mode. I tried raising process priority. I tried launching the game through exe file without being logged to Origin. I tried running the game with edited game setting file (DX12, DX11, windowed mode etc.). I think I tried fow other thing I can't even remember now, but NOTHING WORKED! I was getting ready to give up on the game. Today I logged in, tried Origin game update (no updates for weeks now) and pressed play button and by some miracle the game launched. So far I tried starting the game about 4 times today and the game always started as if it was not giving me hell all yesterday. The remaining problem is that the game now has terrible performance, especially CPU spikes are bad, it's stuttering like crazy and drops down to red numbers every few seconds for no reason. I play the game since launch and the performance has never been this bad. My specs are i7-4790, 16GB, GTX1080Ti, SSD+HDDs checked with HD Tune. I am not used to games acting rogue out of nowhere. After all the martyrdom of trying to run the game yesterday I am really affraid to try Origin repair as it might make the game unlaunchable again.
So my advice is: Do not do anything and try to launch the game after few hours or next day. Hope it helps.