For computers, if you’re in-state, you have a great chance. If you’re out of state, it’s not worth the high tuition cost. Prestige is pretty much a non-factor in technology.
If you are in-state, I think you have an excellent chance. It’s okay that your ECs don’t relate, but it will look good if you have taken four years of rigorous math and science classes, and possibly AP Computer Science classes (if they are offered at your HS).
“Is there really a difference between in/out of state in terms of admissions rate?”
Yes. UIUC is funded primarily by IL taxpayers for IL students. OOS and international students are admitted for diversity, but usually only if they can pay a higher tuition rate than in-state students.
“Why is prestige a non-factor?”
Prestige is a non-factor in CS because tech is so vital to companies’ survival that they must care more that their programmers know what they are doing rather than the name on their programmers diplomas.