Re installing the drivers would be the next thing I’d try. I can’t see how that could cause any further harm. I think I’d reinstall FCP next after that (I think you’ll have to reinstall the drivers again after you do that).
Deleting the prefs with FCP rescue as TCW mentions is easy to try, harmless and maybe worth it but I don’t believe that problems relating to not recognizing the card are to be cured that way.. you never know.
One thing to try if you get desperate is to reinstall everything from scratch on a new drive; buy a new Sata drive, put it in a bay (assuming you have a free one in the G5) and start from scratch; install os x, fcp, and the Blackmagic drivers and see what happens. Working with the new drive you can keep your old drive in the machine and intact in case you decide to go back to it. It’s good to freshen things up now and then, though maybe a long process if you have a lot of other software to install to get up to speed.
Good luck.
jason