Seeking data recovery software for macOS X 10.04

If data has been erased, it cannot be recovered unless it is from a backup disk. It may be possible to take the disk/computer to a recovery service but know that this method is very expensive and there is no guarantee.

I've used Alsoft's Disk Warrior with success in the past. But I don't think it will run under Mac OS X 10.4 (?).

However, if your intent is to use a recovery app on a more recent Mac to recover data from a vintage drive that had/has OS X 10.4 installed on it, then DW may be worth a try.