Is it legal for a 17yr old girl that is now living with her parents to move out and move in with her boyfriend without the parents consent? and can they press charges?

In the state of Illinois, a seventeen year old may legally consent to sexual contact, meaning, it's not likely any charges for sexual assault of a minor would be in your boyfriends future; however, the age of majority in Illinois is still 18. Until you are 18 years of age, (or you are emancipated) you are a "minor" in legal terms. This means that your parents still have legal authority, responsibility, and accountability for the welfare and control of their minor child until the age of 18.

They are within their authority to pursue legal action, where necessary, to maintain control until their minor child legally becomes an adult. Whether they will use that authority is something only you could know. Some parents do, and some don't. If they are motivated, there are probably a few ways they could make legal trouble for your boyfriend if you were to move in with him.