Normally you can have two installations of Photoshop activated. I think you have installed PS on your old PC without deactivated the former installation.
You have to deactivate you installation on the old PC before you activate the installation on your laptop.
BTW: Which version of Photoshop do you use? For older version the activation servers are off. In this cases you have to download special installation files. Take a look here: https://www.adobe.com/cfusion/entitlement/index.cfm?loc=en&e=cs2%5Fdownloads. You need to login with your AdobeID.