MacBook Mac OS X 10.5.8 - won't upgrade to 10.6.8 - Help please!

Question

I have a MacBook (specs below) and purchased the Apple Snow Leopard 10.6.8 CD from Apple, run the installation program, however About This Mac still says that it is running the old version 10.5.8
I have a new iPhone 4 and when I try to plug into iTunes, it tells me to update iTunes, and then when I go to do that it tells me the software is not up to date. This is how I know it hasn't upgraded.
So I restarted the computer and nothing, still says 10.5.8   Can anyone offer suggestions please? Thanks in advance
Model Name:
MacBook
  Model Identifier:
MacBook4,1
  Processor Name:
Intel Core 2 Duo
  Processor Speed:
2.4 GHz
  Number Of Processors:
1
  Total Number Of Cores:
2
  L2 Cache:
3 MB
  Memory:
2 GB
  Bus Speed:
800 MHz
  Boot ROM Version:
MB41.00C1.B00
  SMC Version (system):
1.31f1
  Serial Number (system):
WQ*****0P1
  Hardware UUID:
79536CB5-36F2-5872-A0AE-5B0ACEDAD510
  Sudden Motion Sensor:
  State:
Enabled
<Edited by Host>

Answer 1

10.6 is a paid update via installation disc.  Getting there requires you look at these steps:
https://discussions.apple.com/docs/DOC-2455
Once you get 10.6, you can update to 10.6.8 for the latest iTunes compatibility.
This will not give you full iCloud compatibility:
https://discussions.apple.com/docs/DOC-2551
However, you should be careful as far as updating to 10.7 or later, because of this:
https://discussions.apple.com/docs/DOC-6271