Mentors don't necessarily come from sponsors. Parents and teachers are just as capable of being mentors. A mechanical mentor can be anyone with experience building things and putting things together. Similar for an electrical mentor. So don't think you HAVE to get professional mentors.
Also, Corpus Christi is filthy with petroleum industry. You're surrounded with mentor potential, you just need to reach out a bit to some local companies to see if anyone is interested in volunteering their time. Your chamber of commerce isn't as useful as I'd like, but these guys look like a good opportunity:
http://www.maverickengineering.com/
Call tomorrow and ask to speak to someone in public relations and give them your elevator pitch and make clear you're not necessarily looking for money, but volunteers as well.
Also, as Jane Young asked in another thread, where are you guys going for kickoff? If you're headed to Houston, I've got some people here you should talk to. Actually, if you're headed to San Antonio, I've probably got some people you should talk to there as well.
EDIT to add:
You've got some other teams around you down there. 2787 - Innovation Academy for Engineering, Environmental & Marine Science, has a few years experience.