Grad school admissions work differently from undergrad schools, mate. Unless you're exceptional (3.68 is unfortunately, not) you can't realistically expect to apply and hope for an acceptance to a 5 year engineering PhD program. It's all about connections. Begin by talking to professors, they are your best resource. Find out where alumni from your college are and talk to them. VISIT the university you're applying to and make contact with a professor in a field you're interested in. In the end you'll be working with a professor, and he won't be simply be picking the best application from the pile. Only the ones that show the most interest, or have been recommended by a faculty who knows someone at the uni, or who are liked by the professor are given admission.

And yes, you should be able to "change" your major if you are accepted into that field. Perhaps not the easiest thing to do though because of the extra number of classes you will need to take to catch up.

Note: This doesn't necessarily apply to graduate programs in other fields or programs where you actually pay tuition.