That MacBook never came with 10.6.3, of course.
The commercial 10.6.3 DVD should install without any problems.
However, the error that you get may mean that you have a 10.6.3 DVD that shipped with another Mac, such as a 2010 MacBook, or a 2010 iMac. Those came with installer DVDs that were special builds of 10.6.3, different from the commercial install, because of new hardware in those 2010 Macs.
Is there any possibility that the DVD that YOU have, really came with one of those 2010 Macs?
Where did you get that DVD?
A new DVD for 10.6.3 is only $20, direct from Apple.
http://store.apple.com/us/product/MC573Z/A/mac-os-x-106-snow-leopard