Sounds weird.. Maybe you can list your pc specs and peripherals, sometimes something really stupid (Speaker-, Microphone- or webcam-drivers can mess with some programs) But it probably isn't the case since it is only online? Also how'd you play offline? Via the forged alliance.exe in the faforever bin folder? Via your CD or just playing Solo in an Faforever game? Maybe try see if it only crashes if you aren't hosting?
Also... Have you actually bought the game or have you torrented it, sometimes really stupid issues like this can occur when faf tries to overwrite the cracked patch, or you just downloaded a corrupted file. If you've actually bought it, try filling in the CD-Key in Steam. Just go to Games (Upper left corner) then select 'Activate a product on steam' and it'll prompt you to put in your CD-Key. Then download it through steam and delete the CD install, maybe that'll fix it because your CD was scratched or something.. If that doesn't work and you don't like Steam? No problem, your Forged alliance CD-Key can be used infinitely on any CD install so feel free to reinstall it on your PC and delete Steam, even though I highly recommend all PC gamers to stop using CDs and use Steam for anything that's available on there
Sometimes, I just feel like I want to eat pancakes.