I know you don't want to hear this, but the only way you can access the paid sites is for you to pay their fees and set up your own user name and password. For anyone else to share their user information violates the terms of their respective contracts, and is basically stealing. Some large libraries provide institutional access on site. Those are free for you to go in and use because the library has paid for the privilege. However, they aren't available from your home computer because that isn't the part of their contract. College libraries may or may not provide access from your home computer. It depends on their contract with the respective companies.
I'm sorry to have to deliver the bad news, but we cannot break contract agreements.
Please let me know if you have questions.