This is how I fixed my XBox 360's RRoD problem:
First, take two screwdrivers, the XBox and the power supply to a table. The screwdrivers should be able to fit in the vent holes in the back of the system. Alternatively, use Q-Tips that have no fluff at the ends of them.
Next, take both the screwdrivers (or Q-Tips), and put them in the back so that it blocks the fans from moving. Power on the system.
Wait for about five minutes. The XBox should change from a 3-ring RRoD to a 2-ring RRoD, meaning that it overheated.
Now, unplug it, remove the screwdrivers (or Q-Tips) and allow the XBox to sit for 15 minutes. Hope for the best.
After 15 minutes have passed, plug it back in, and power it on. If it works, good job.
You'll probably want to eventually take it apart and fix the X-Clamps and all that, replace the thermal dye and whatnot, but this should let you be able to play your games without wrapping your XBox in towels and creating a fire hazard.
Also, a little disclaimer: I will not be responsible if you break your XBox doing this. This worked for me, but I have no guarantee that it'll work for you. Do this at your own risk.
