I was able to boot from the Tiger DVD, and I opened up Disk Utility, but no Hard Drives were listed.
The only other Mac that has FireWire is a Beige G3. I don't know if that would work.
Rescuing data is crucial.
Oops. I mean, really. Disk Utility not seeing your drive is usually really, really bad news. :'(
Try to boot the iBook in target mode (T pressed at startup until you see a purple logo and the FireWire logo). The G3 shouldn't have any problems mounting your iBook's drive, as long as it's not dead. If it can't, again, bad news.
Does the drive make any unusual noise? Or, does it still make any noise? As equiil said, what you described is very consistent with a fatal hard drive failure.
Some were lucky in making their broken drive work long enough to backup crucial data by cooling it several hours in the fridge, but I sadly never was. Irrelevant for an iBook, but pretty cool to see is
this old news from the french site macbidouille.com. It basically says that the guy was able to get his data back using those cooling plates, changed every hour. Copying 20 Gb of data from his failing drive took 28 hours at an average 200 Kb/s.
Sorry for those bad news… but to end on a positive note, I have to tell the story of a friend of mine loosing some pretty important data from an iBook G4 a couple of weeks ago (one week of work since the last backup). Just as yours, his drive wouldn't show up in Disk Utility nor from another Mac, nor when booting the iBook from an external HD. Then a few days later, when he had already ordered a new drive and begun his work over, the faulty drive suddenly mounted after a reboot. He immediately copied everything on the external HD. A few more reboots, and the drive was gone for good in Digital Heaven.