I'm not sure why you mention a burner at all when your intention is to back up to an HDD.
There are guides everywhere so I'm not sure how managed to miss them but here's how it's done:
1 - Install a custom firmware which can only be done on firmwares 3.55 and lower. Kmeaw 3.55 and Rebug 3.55(.2) are the most popular.
2 - Install a game manager, there many of these to choose from.
3 - In the game manager there is an option to copy the disc to any other device it detects and of course that includes the HDD.
I could break down each step but a lot of it is self explanatory and more importantly... regardless you would want to see a video to see what it's like first rather than just read about it. It's a very simple process and there are tons of videos out there.
In the off chance that you don't know, installing a custom firmware means no more network access. Attempting to log in would result in it telling you to update to an official firmware and will most likely get you banned sooner or later.