Since your machine works, it's probably not a big problem.
First, while in finder go to the Finder menu and select Preferences. Make sure the Hard Disks is checked under "Show these items on desktop".
If that's not the problem, go to your Applications Folder and then Utilities. Open Disk Utility. Any drives will show up. Click on Macintosh HD and see if there's a Mount Button at the top of the window. If there is, click it.
Using OSX 10.3.9 & 10.4.11 on a G4, G5 & Intel Macbook