The big companies mostly license music from other companies and/or outsource to independent sound designers. SFX are a different story as most companies own massive SFX libraries. Our company Gamecues.com is a music licensing site strictly for the gaming industry. We have signed on a few big artists as well as many indie artists. At the moment we are not taking submission though because we have soooooo much music sent to us we can't sort it all out in time.
My advise to the poster is to contact as many music licensing companies as possible about sending them you samples of your work and make contacts. Many companies aren't accepting submissions all the time but it can't hurt to have your info in their database.
Hope this helped.