Xbox – Will buying a digital full game from the xbox live marketplace still keep the data on the hard drive

You need to get a Hard Drive Transfer cable which will copy everything, including your save games, onto the 360 slim (assuming there is enough room on it). You don't need the bricked 360, just it's hard drive and the new slim xbox. You can also do this with just a USB drive, but will take longer depending on how much you've got to transfer.

If you've purchased a new Xbox 360 console, you can transfer everything (games, videos, music, saved games, gamertags, and even your hard-won achievements) to your new console!

There are two options available for moving your precious information. You can either use the Xbox 360 Hard Drive Transfer Kit to move everything to your new console, or connect a USB thumb drive if you only have a small amount of content such as your gamertag and saved games.

As you'll only use it once, my advice would be to buy one off ebay where you can then sell it again after you've used it for near enough what you paid for it.

As for the xbox itself, it sounds like it's overheated and the graphics card has started to warp and come off the motherboard. This problem can usually be fixed by clamping the card back down via a bit of DIY and a few bolts. If you don't fancy doing it, there's usually a few people on ebay that do this themselves and would be willing to offer you some cash for it ;)

Yes, with a few exceptions. Forza 3, for example, comes on two discs but one of the discs is data, so if installed, disc changing is not necessary.

The reason you need to insert each disc is a way of making sure you possess the physical game disc at the time you are playing.