Where did you get OS 10.6.3 from?
Have you confirmed that your computer meets ALL of SL system requirements?
Disconnect all devices from the computer then do the following:
Boot up from your Snow Leopard Install DVD while holding down the "c" key.
Select the language you wish to use, and then choose "Disk Utility" from the menu bar.
Your HD should appear in a panel on the left hand side of the window which opens. Select it and then click on the "repair disk" button in the right hand section of the window.
Once this process has been completed restart your computer and repair permissions directly from Disk Utility.
If Disk Utility is unable to complete the repair, you will need to use a stronger 3rd party utility like DiskWarrior, Techtool PRO (not Deluxe) or Drive Genius.
The error just says OS cannot be installed.
1: Make sure the bottom of the 10.6 install disk is clean and polished with a soft clean cloth and a tiny bit of rubbing alcohol to cut the finger smudges (oil)
2: When you c or option boot, use Disk Utility and select the ENTIRE drive on the left top (drive makers name and size) then click Erase and Security option > Zero All Data, come back in a hour.
3: Head to Partiton and 1, option Guid and format OS X Extended Journaled and click apply.
4: Quit and OS X should install, if not the disk and/or drive is defective.
optional: For Snow Leopard Speed Freaks