Uh, yeah, knowing how you are going to PAY FOR IT is the most important part of choosing a college that is right for you.
So, this means you really only have one option:
You need to log onto the fafsa website and click "Add a School Code" TODAY and enter another (Cheaper) school to your fafsa because without a cosigner with awesome credit and a very high income, you will not be able to take out a private student loan.
I want to know why you have been SITTING on this little tidbit of a barrier (money) since friggin April? LOL Apparently you didn't want to go THAT bad. In the adult word, money doesn't start falling from the sky when you want something you don't have the money for. Realize that when you don't pay by the deadline, your school drops all your classes and if you signed up for a dorm, they usually put another student in your room in your place. This means you loose all your deposits and any other money you put up front.
The bad thing about this is that even if you add another school code today, you won't be able to get everything processed at the cheaper school in time there either. Meaning you will have to pay CASH at the new school. Stinks not thinking ahead here.
In short:
NO, no way you can get a private student loan without a cosigner! It sounds like you need to find a job today and start saving your money if you still want to attend Penn State. Be aware you will be in college for FOUR years... meaning you will need 20K times FOUR years... it may take you more than a semester to save $80,000 Learn from your mistake and plan better for the spring.