MOE uses grants to (partially) fund their FLL/JFLL/VEX tournament each year. There are many corporations that have them but sometimes it takes a bit of searching to find them. Be aware that you have to specify either a school or your 501c3 EIN number to qualify - you probably won't be able to specify FIRST's EIN number.
That said, there are many that you can try. Here are some that I still have bookmarked (although they haven't all given us money
Verizon
http://foundation.verizon.com/04007.shtml
Daimler Chrysler
http://www.fund.daimlerchrysler.com/
Nestle
http://npd.nestle-watersnasponsor.com/
JPMorganChase
http://www.jpmorganchase.com/cm/cs?p...obtain/contact
Wachovia
http://www.wachovia.com/inside/page/0,,139_414,00.html
There are others that I don't have the sites: JCPenny, Bank of America, BestBuy (they give products only), Target. We haven't seen any government grants but then we haven't looked either.
The online grant process is tedious but you can get money this way.