I've never seen the connection from the logic board bad on the board. Your best bet is that it's a simple bad hard drive. The computer sees the drive, ergo the cable and connection are probably good.
Here's how to replace the drive: [guide|208]
Here's a couple of ATA drives that will work for you: http://www.ifixit.com/Mac-Parts/PowerBook-G4-Aluminum-12%22-867-MHz#0-Hard+Drives+PATA+