You should not need to install CS2 on your new computer if you have the original serial number in hand.
You begin installing CS4 upgrade CD/DVD. During the installation process it should prompt you to scan for a previous install of CS or to manually enter the serial number from your CS2 install disks. You should have the serial number stickers in the original documentation of CS2. After you enter that serial number, CS4 will ask for the upgrade serial number from the CS4 documentation. After that, you should be done. (after the obligatory software updates, that is)
NOTE: CS3 can be installed on 2 different computers. The software must be activated with the Adobe serial number server. CS1 requires no serial server activation. If CS2 required activation with a serial server, and you no longer wish to run it on the old computer, you should probably deactivate that serial first, before doing the install. Directions for deactivating the serial number so that you can reregister on another computer can be found on Adobes site.
And next time people...how about cutting some slack for a new poster? Do you really need to feel the need to chastise someone and not even bother to offer to help afterwards? That's just bad manners.