If you only have access to online, but no printer (we've been there) you can check in 24 hours in advance and then get the ticket printed out at the kiosk/desk at the airport. You still have the ability to get the "A" seating, but don't need full access to a computer.
That way you can also have someone who does have access, check in online for you a day in advance and get the "A" as well.
Southwest even has a simplified version just for cell phones so people can check in more easily, without the browser locking up or not loading right. Just don't forget to bring your confirmation number with you (though we found they were really nice about looking it up for us via phone)