Easy bit first:
An external DVD writer is a 'plug & play' device. Just plug it into a USB port and you'll be ready to go. (The only problem with having an external DVD drive is that it's easy to forget where you've put it. I've spent several hours today unsuccessfully trying to find mine!)
With regard to the internal drive though, in what way isn't it responding? When you go to 'Computer' is it shown there? If so, when you put 'Carry On Up The Khyber' (or any other commercial DVD) into it, will it play? [I'm trying to eliminate the burning part of its job here].