You can forget about UIUC for any aid from OOS.
For Purdue, they do have a significant number of merit scholarships granted each year even for OOS students and no separated application is needed (must apply EA). The Trustee scholarship is $12k-$16k per year for OOS (150 awards including OOS) while the Presidential Scholarship is $5k-$10k per year for OOS (~1100 awards per year including OOS).
ACT 35 would be at the threshold for Presidential Scholarships but many did not get it last year with that score though. Weak EC would hurt his chance on merit scholarships. A girl applying to engineering may also improve the chance for scholarship. My D with 4.0/35 got the $10k Presidential Scholarship last year plus another $10k/year scholarship with a need component.