1) Send your console in to a big corporation, wait a month, and get a console that'll break in another month.
2) Throw it out or try and sell it. You could make $40 or so and put it towards a new console.
3) Try and fix it yourself. Now there are several paths you can take to "fix" your box, and hopefully this instructable will make this task less daunting (and explain the right way to do it)
So lets get started!
Step 1: Fixes that DONT WORK
The Towel Fix-
People think that by wrapping their 360 in a towel and running it for excessive periods of time, the internal components will reach the melting point of lead-free solder (217C), and the bad joints under the BGAs will reflow, fixing the problem... I'm not even going to explain what's wrong with that picture.
The Penny Fix-
By putting pennies underneath the GPU heatsink/on top of the RAM chips, the extreme pressure on the RAM BGAs will (in some cases) push the chip down enough that the bad joints make connections. Now this is all good and dandy save the fact that neither the solder balls nor the RAM were meant to take that kind of pressure, and this fix will only lead to more broken joints.
The "X-Clamp" Fix-
This fix utilizes the same basic principle as the penny fix. By removing the stock heatsink clamps, you can hold the CPU and GPU heatsinks on with machine screws. The idea is that you can over tighten the bolts causing the heatsinks to exert more pressure on the processors, pressing the broken solder joints down until they make connections. The issue with this is that more pressure inevitably leads to more broken joints... which leads to more pressure, which leads to more broken joints... the vicious cycle continues until you get micro fractures in the chips and your console is dead for good.