The sandbox is an independent phenomenon, I’ve seen sites that are PR6 but still in the sandbox. New sites are put in the sandbox for a probationary period. No one knows for sure what triggers the sandbox, or how exactly you get out of it, but most people believe you just keep building links and after enough time passes you are released. The sandbox prevents your site from ranking well for any competitive keywords, again, no one knows how Google determines what is competitive or not, but for certain most gambling terms are.
PR has to do with your backlinks and the quality and quantity of them. Your site is probably not showing PR because it wasn’t indexed until after October or whenever the last PR update was. Google updates the “visual” PR every 3-4 months, while the “real” PR is kept behind the scenes, so you will get the benefit of whatever PR you have, just not be able to see it until the next update.
As for backlinks, Google does not display all of the links pointing to your site, likely because they don’t want people reverse-engineering their algorithms. For an accurate count of your backlinks, you should check Yahoo.