Other than hitting up the rotary club/chamber of commerce/school board (which has already been mentioned), here's what I would suggest.
1.) Play the "6 Degrees of Separation" game with your team. Sit everyone down (students, mentors, et al) and make a listing of where everyone (or their parents, for the students) works. Write them all down on a big whiteboard/piece of paper. Then work one step beyond: Where does everyone's relatives work/have worked? If multiples start showing up, just make a note of how many connections you have with that company. Then, move one step further and ask whom everyone knows in the area that are in high-level positions in their company. At this point you should be able to have a good list of companies to pull from, whom will be already emotionally involved somehow because they know someone on the team.
This is the process that Babson uses to get Commencement speakers; we got Ted Turner to speak at Commencement 2002 because come to find out, his goddaughter was getting her undergraduate degree that year....but the connection wasn't made until the committee actually sat down and said "who do we know?"
2.) If that doesnt work...
http://premium.hoovers.com/subscribe...it eDisplay=P
Here's a listing of all the major corporations in the Warren-Detroit area. Let me know if the link doesn't work for you and I'll export the list.
Also:
http://www.city-data.com/city/Center-Line-Michigan.html I would suggest adding the local press/tv & radio stations listed here to the list of companies to contact, as well as the colleges listed.
3.) Research company addresses/names of executives (
www.hoovers.com is your friend!). Companies are more likely to read a letter if it's actually addressed to someone in the company.
4.) This would be the point where I would suggest a mail merge & letter stuffing party. With your shortened time frame, however, I would suggest utilizing email if you can find their email. If not, then mail companies closer to you (Warren area) as opposed to further out.
If it takes you more than 30 min to drive there, it's not worth it at this point unless your team has a personal connection (what you found in step 1). According to the City Data link I posted above, the mean drive time to work for people in Center Line is 27 minutes. Thus, it is safe to assume that any company within 30 min driving distance would know of Center Line because they are more likely to have someone who works with them from there.
5.) Follow-up call on all the companies you contact. Grab a couple bottles of Mountain Dew, make a bag of popcorn and have a phoneathon with your teammates. Introduce yourself (I am <name> calling from the Center Line robotics team), ask if they recieved the letter, and if they would be interested in giving any size donation. Mention that you have a shortened time frame and that the community is getting behind you guys since it is so exceptional that such a young team could accomplish so much in a short amount of time. I can help with a scrpit if you need it.
Good luck, and let us know how it turns out!