The class I want is full, is there any way to get into it?
When a class is full/closed you have two options. Your first option is to wait until late registration when seats become available due to purging of the students who have failed to pay their fees by the deadline. The second option is to approach the department that is offering the course and ask to be permitted into the class. A permit/override can only be authorized by the department head under which the course is being offered.