I know how to fix it, i fixed my brothers last weekend.
ITs normally related to the CPUs been soldered onto the mainboard, instead of into a socket. Add to this reports that some were put together with incorect thermal blocks been put between the heatsink upside down! What can happen is you get a "dry" connection, and the solder doesnt work right on the connections.
SOme people have tried things like wrappging their 360 in a towel and over heating it to help fix the connections, or takeing off the heat sink to over heat the cpu. This didnt work for me, so what i did...
Grab a blow tourch! - the truth!
Blast the heatsink so that it gets so hot the heat passes through the sink and cpu into the legs and the soldier. this then helps rpair connections and hey presto it worked again Smiling