Question Bring my desktop to another country

You need to list all of your components aside from the case.

But generally, you should remove the CPU cooler (especially if it's a big tower cooler) and any add-in cards (e.g. GPU, wireless adapter, sound card, etc.). Those things can go in your carry-on luggage and the tower can go in the checked bag (you can have extra protection by filling the case with packing foam or air bags).