Are you moving from one dotnetnuke instance (separate code/database) to another DNN instance? Or are you working within multiple portals of the same instance?

It's possible the skin itself requires some library files that may be in the BIN folder at the root of your website, but without looking at the skin itself (the ascx source) I couldn't really tell you which ones.

Are the versions of DNN the same between the two?

On the host/extensions page (as a super user) go to the Actions menu next to the extensions module and click on the Install Available Extensions option, there you will find a list of the core modules that aren't installed by default.

As for other modules, those won't be easy to just copy and paste like the skin was. Many modules require installation scripts and processes to be run during the installation, those won't be completed by simply copying and pasting the modules. You will need to have the install packages for the modules in order to get them on another site easily.