I am applying to an Illinois University for my Bachelor's in Early Childhood Education. Unfortunately when I was younger and stupid, I got a DUI in Illinois and a DWI in Missouri. I had an attorney for both and got them "taken care of". BUT, I know they are probably still on my record, right? If the University does a background check, will they find these charges? If so, will that hurt my chances for acceptance into the University and later hurt my chances for a career in that field?

If it was a documented court case and not expunged then yes they will show up. That's what background checks do.

You say you "got them 'taken care of' ". Does it mean that you weren't convicted of the charges? If so, it shouldn't affect your licensing chances. Whether the university considers this when you apply for admission is up to them. You had best be prepared to explain the record in the best light.

I agree "taken care of " is not a legal term and we have no idea what was done.

So run a criminal background and a motor vechile report on yourself and see what shows up.

Fingerprint check will show who you are and if you were ever fingerprinted under a different name.

Criminal background will show any criminal conviction on your record.