As far as sponsorship goes, don't limit yourself to obtaining sponsorship from one department or office. Many are willing to help out! Also - Don't eliminate departments and offices just because they aren't engineering-related.
Find whatever office supports your college's student teams. Even though they may not fund things that directly benefit the high school students, they may take care of the mentors' travel, food, etc.
There is also probably an office that handles corporate sponsorships for your college. Find them, and see if they'd be willing to connect you with some of those sponsors.
Since most of the mentors may be college students, it is beneficial to do several "How to Mentor" trainings before the season so that the mentors don't get pulled into thinking they are high school students again and and end up taking away from the learning experience. It is very easy to get caught in that trap.
I've mentored/run a college-sponsored team for the past 7 years, so if you have any specific questions, feel free to let me know!
