I've looked at my Tiger manual. I'm assuming that you have booted from the install disk by holding the 'C' key down during boot. You would then run Disk Utility from the install disk. When you click on the 'First Aid' tab there should be a column on the left in which the name of your hard disk should appear. If it's there, click once to select it and then the 'Repair Disk' button at bottom right should become clickable. You may be able to get the disk working, but if you can you should copy data off immediately as it is likely to fail at any time.
If your hard disk does not appear in on the left then it has presumably failed and so Disk Utility can't see it it. If this is the case I doubt you are going to be able to retrieve anything from it. There are firms who offer rescue services and may be able to retrieve data but it's liable to be very expensive. There are other programs such as TechTool Pro and DiskWarrior which are more powerful than Disk Utility but they're not cheap and if the disk has actually failed they won't do any good - they can only repair Directory corruption.