If you do not have the discs that originally came with your computer...
If you're not in the US, you may need to go through the regional Apple Store that serves your location to find the contact number - http://store.apple.com/Catalog/US/Images/intlstoreroutingpage.html
A replacement disk you get won't be 10.6.8 anyway - I think it's 10.6.3 and then you have to download the combo updater to bring it up to 10.6.8. If your Mac is rejecting your install disk it may well reject the replacement, though it's not that expensive and miught be worth a try. Otherwise you may have a problem with the disk drive and that would require the attention of a service engineer. If you can get to an Apple Store you should make an appointement to see them - they may be able to sort it out for you or at least identify the problem.