It sounds like your old laptop used Creative Suite, which came bundled with a variety of fonts. Creative Cloud does not come with a package of fonts, but most Creative Cloud memberships include a Typekit Portfolio plan.
Here's more information about which plans include Typekit Portfolio: Typekit Requirements
We have an article that explains how to sync fonts to your desktop for use in Adobe programs here: How to sync fonts
Let me know if you have further questions.
How can I get the Creative Suite fonts?
You would need to uninstall Creative Cloud and install Creative Suite.
How can I download Creative Suite, everything takes me to Creative Cloud.