With the 10.4 Install Disc...
"Try Disk Utility
1. Insert the Mac OS X Install disc, then restart the computer while holding the C key.
2. When your computer finishes starting up from the disc, choose Disk Utility from the Installer menu at top of the screen. (In Mac OS X 10.4 or later, you must select your language first.)
*Important: Do not click Continue in the first screen of the Installer. If you do, you must restart from the disc again to access Disk Utility.*
3. Click the First Aid tab.
4. Select your Mac OS X volume.
5. Click Repair Disk, (not Repair Permissions). Disk Utility checks and repairs the disk."
http://docs.info.apple.com/article.html?artnum=106214
Then try a Safe Boot, (holding Shift key down at bootup), run Disk Utility in Applications>Utilities, then highlight your drive, click on Repair Permissions, reboot when it completes.
(Safe boot may stay on the gray radian for a long time, let it go, it's trying to repair the Hard Drive & clear caches.)
If perchance you can't find your install Disc, at least try it from the Safe Boot part onward.
Highest OSX you can run is 10.5.8...
Leopard requirements/10.5.x...
* Mac computer with an Intel, PowerPC G5, or PowerPC G4 (867MHz or faster) processor
minimum system requirements
* 512MB of memory (I say 1.5GB for PPC at least, 2-3GB minimum for IntelMacs)
* DVD drive for installation
* 9GB of available disk space (I say 30GB at least)
Classic/OS9 Apps no longer supported.
May be available from Apple again...
https://discussions.apple.com/thread/4720126?tstart=0
Trouble is Apple no longer sells it, check eBay & such for the Retail version, not the Gray Discs...
http://www.ebay.com/sch/i.html?_nkw=mac+os+x+leopard+retail+10.5
There are workarounds if the 867MHz CPU is the only hangup...
http://sourceforge.net/projects/leopardassist/
http://lowendmac.com/osx/leopard/unsupported.html
List of Applications Not Compatible with Leopard...
http://guides.macrumors.com/List:Applications_Not_Compatible_with_Leopard