Without knowing your exact machine I can not tell you the range of Mac operating systems it will take. That given. all will run 10.4, Best if you have the original system installation disk. Insert the disk, restart and shove the disk back in and hold down the "C" key. Go to the second page and the pull down menu will appear. Go to disk Utilities and run Disk Doctor and see if you can repair the hard drive.
Either your system is corrupt, has the wrong system or hard drive has gone bad.
Disk Utilities failing, I would then reformat the hard drive (using the "write zeros option, to map out any bad blocks), Then reinstall a new system.
If you do not have the installation disk, you will need to give us your exact machine. That information should be printed on the back or bottom of the machine. Then we can direct you to the correct system to install and where to get it.