Battlefield 3 won't load online game (Black Screen) PS3

My bet is that is is related to your extremely slow connection. You can try a couple of things to try to improve your speed such as hardwiring your console to your router for a faster direct connection instead of using wireless, and I recommend resetting your router by turning off your router, unplugging it, let it sit unplugged for a few minutes and reboot it as that often helps connectivity issues.