I just purchased an Xbox 360 Elite today (July 4th), brand new and everything.
With it I also purchased Mass Effect, The Orange Box, Grand Theft Auto IV, and Burnout Paradise.
My main problem here is that my GTA IV keeps freezing. I haven't barely even started the game yet. Every time I step out of the Roman's apartment, the game just stops. It's a brand new disc too, so what do I need to do? (same problem with Burnout Paradise)
Try a new copy of the game. Failing that, make sure your Xbox360 is well ventilated, not on a carpeted surface or caged in by a little wooden cabinet or something.
GTAIV loads data differently to almost all other games (GTA always has). It preloads the areas it THINKS you'll like to go as you're going in that general direction, in order to make the world seem like one big expansive place. Oblivion does the same thing.
Because of this, it puts a large load on your DVD drive, so it still could be your 360.
Try a new copy, if that doesn't work, get a new 360.