Don’t do it! There’s a 97% chance it will fail.
If anything does go wrong you will loose your warranty!
You don’t need to put your old hard drive on, just recover your gamer tag to that 360. Then you can download all of you DLC back for free. I am afraid your saved games are all but lost since your 360 died
(Usually you would use a transfer cable or USB)
Just don’t do it, I got the slim too and had to loose all my saved games but I would not risk loosing your warranty and busting you Xbox. I can give you some websites on proper ways to get your new 360 and DLC back the right way way.