Installing Minecraft on the new computer is not a problem. Have the key and everything. But how do I get my current score on the new PC?
Do not need a key to Minecraft on another computer to install
Open the ".minecraft" folder located at "AppData" (Windows + R and enter "% appdata%"). There you will see a "saves" folder, there are all your worlds stored in it. Can copy the entire folder to your new PC.
Do you mean your world?
In Explorer, navigate to% appdata% and then to ".minecraft", then you can copy the "saves" folder into your new .minecraft directory.