Man... Upgrade to a new PS2 and a Magic V
What kind of media are you using? If all your other games are working okay, you may have also have a bad, or too scratched up Hitman game.
As for the EA games. I can't help. I don't know too much about Swap stuff. All I can say is that I've not had a problem backing up Hitman 2, or several of my EA games including NASCAR 2004, Madden 2004, and NBA Live.