Q: I have a G5 running Leopard. Trouble starting. Hardware good. Cannot reinstall OS X. Error message 'Disc is damaged'

That message refers to your hard drive, not the DVD!

You cannot perform repairs from the same start-up disk. Reboot from your install disk (holding down the C key). Once it opens, select your language, and then go to Disk Utility from the Utilities menu. Select your hard disk as before and click Repair:

http://support.apple.com/kb/HT1782?viewlocale=en_US

Once that is complete reboot again from your usual start-up disk.

More useful reading here:

Resolve startup issues and perform disk maintenance with Disk Utility and fsck

http://support.apple.com/kb/TS1417?viewlocale=en_US

For a full description of how to resolve Disk, Permission and Cache Corruption, you should read this FAQ from the X Lab:

http://www.thexlab.com/faqs/repairprocess.html

Apple's advice on general maintenance:

http://support.apple.com/kb/HT1147?viewlocale=en_US