I'd like to welcome you to Chief Delphi! I've found that it's a great place with a lot of helpful people.
I can empathize with the search for funding. Our team has been working very hard to raise money. We weren't at all sure until about a week and a half ago that we would be able to attend our regional. For months, I had visions of paying at the last minute.
As Akash mentioned, the deadline has passed for BAE. The application instructions are here -
http://www.baesystemsfirst.org/regional/pdf/grants.pdf Perhaps you can put together a team calendar specifically for fund raising and include BAE for July.
Our team has pretty much tried it all. We've written donor letters requesting funds. We've approached area businesses. We've had tag sales and sold Tupperware. (Don't laugh too hard about the Tupperware, the turnaround on getting your check is faster than many other organizations.) We had a demo at the county fair and put out a donation jar. We've written grant applications. We put a PayPal button on our webpage.
I know that teams have tried all sorts of creative fund techniques. Perhaps you could ask a Barnes & Noble if you could have a fund raising day? One team recently posted their B&N fund raiser information here on CD. If that won't work, maybe your team could man the gift wrap station at the bookstore and collect donations? When I was shopping on Black Friday, there was a charitable organization doing just that.
Could you organize a Lego building party for local children one evening so parents could shop without children in tow? One of our local private schools used to do that. The kids loved it, parents happily paid and the school wasn't using the space in the evening so it was a win/win situation.
Have you considered the ever popular pasta dinner? There's some useful information on the NEMO site here:
http://www.firstnemo.org/resources.htm
I know there's not a lot of time so perhaps the first task might be asking FIRST for an extension. I tried to find the post where someone mentioned being granted one until the middle? of December.
Good luck! I hope that something comes through for you soon. I know I've been going to our team mailbox for a couple weeks now hoping that a promised donation will be there. Hopefully a donation will come through for you too.
Trying to Help