“Eligible institution” means:
1. A university, state college or community college within the System; or
2. Any other nonsectarian college or university that:
(a) Was originally established in, and is organized under the laws of, this State, or operates a clinical program within this State in which students enrolled in the college or university receive training;
(b) Is exempt from taxation pursuant to 26 U.S.C. § 501(c)(3); and
(c) Is accredited by a regional accrediting agency recognized by the United States Department of Education.