This is the Ghetto way, but should get it running again...
(Mind you I buy 360's by the pallet broken, fix and resell, last pallet was 80)
1. Turn it on.
2. Take a hair dryer, HIGH heat LOW SPEED.
3. Point it into the rear vents about 6" away from it, depending on strength of heat from blow dryer.
4. Keep an eye on the rear plastic and try not to melt it (Its easy to do when you get it real hot, and that is what you want to do here.)
5. After about 2-2.5 minutes place your palm on the top of the 360, make sure it got nice and hot in there, we want over 100c right around to 110c the melting point of the solder is like 126c. Dont worry you wont break it worse.
6. While the hair dryer is still running turn off the 360 and back on (Remember you want to be heating it up while its running not while its off). If it dont boot continue turning it off and back on until it does. That should reset the internal protection.

WTF didnt post! Better this time!