As a Silver XBLA user, what data will I lose when I replace the Xbox 360?

My Xbox 360 is giving a 3/4 red ring (the top right is un-lit) and turning itself off shortly after logging into XBox Live. (It's way out of warranty.)

If buy a new Xbox and re-sign into my XBLA account (It's only a Silver account, with no Cloud storage) on the new one, what data will come over from the old Xbox? What data will I lose without using a hard drive transfer cable from the old Xbox?