sanddrag,
You basically need to talk to the LA Regional Director. I've no idea who this is. I'd recommend emailling FIRST at
info@first.org and
volunteer@first.org. Make it prominent that you're arranging to have a webcast donated to the LA Regional. Say donation a whole lot, as I hope that'd get their attention. Ask for full contact info for the LA RD or someone in charge of fundraising for the LA Regional.
Mostly, I think you need to present yourself as arranging a donation to get their attention before you ask about them providing an internet connection. And remember that FIRST Corporate is in a bit of flux at the moment with new board members and whatnot.