By reading your descriptions and attempts, I highly recommend you contact a professional data recovery service like Drive Savers or Ontrack, as both vendors provide free estimates and both are recommended by Apple.
No normal data recovery software like iBoysoft Data Recovery Software is capable of recovering data from a failing hard drive as badly as yours since apps and even Apple support cannot handle the physical hard drive error.
Another chance you can take a risk is to clone the hard drive to a functional one and then retrieve data from it instead, yet this way only gives you the original data stored on the problematic G5 HDD. In other words, the data will be as broken as the ones in the failing drive. There is no way to repair them. I sincerely hope you are lucky enough to get all the data successfully.
Finally, even though I have stressed the importance of backup to so many people, I have to mention here again, please do BACK UP your computer and any external hard drive since hard failure or data loss accidents always happen without a sign!
