The license you have only covers one computer, and the install disks from one type of Mac will not work on another type. You need to buy another copy of Snow Leopard.
Start by checking if it can run Snow Leopard:
Requirements for OS X 10.6 'Snow Leopard'
OS 10.6 Snow Leopard is once again available from the Apple Store:
and in the UK:
but nobody knows for how long it will be available.
To use iCloud you have to upgrade all the way to Mountain Lion:
You can also purchase the code to use to download Lion (Lion requires an Intel-based Mac with a Core 2 Duo, i3, i5, i7 or Xeon processor and 2GB of RAM, running the latest version of Snow Leopard), or you can purchase Mountain Lion from the App Store - if you can run that:
When you have installed it, run Software Update to download and install the latest updates for Snow Leopard.