I have a pretty old Xbox 360 here without HDMI and a pretty small hard drive. I'm thinking of upgrading to an Elite. Now how do they go about with my previous downloaded games? Will I have to order one of those cables and transfer it all or can I just redownload them? Are there any potential problems going from one machine and hard drive to another set even though I'll be using the same profile?

The Elites don't come with a cable transfer, so you will have to transfer the game licenses to your new system on Xbox.com.
 
It's pretty simple, but you will have to do the process one at a time for your games and DLC.  A definite pain in the ass if you have a lot of Rock Band songs.  As for game saves... you will need to get a memory card to transfer them over.

Ah, I thought you had to order a cable and do a physical transfer. Shame about the save games and memory card though since I don't have a memory card. Although I think I can probably borrow one from a friend..

" Ah, I thought you had to order a cable and do a physical transfer. Shame about the save games and memory card though since I don't have a memory card. Although I think I can probably borrow one from a friend.. "

u can redownload the things u bought on xbox live. i would suggest go to gamestop or something buy a used memory card and get all of the saves onto there. a few days later u go back tell them that it doesn't work so u can get ur money back.