The parking office may be closed on the day you arrive (e.g., Memorial Day). You can simply go to the office the following morning.
Note: summer parking passes are distinct from those issued for the academic year, and the registration/purchase process probably will be, too.
Make sure you follow all instructions and meet all deadlines for fall parking, regardless of whether you are bringing your car to campus for the summer.
Visit the Ole Miss Parking website for more info & instructions.