Modded Xbox 360 4 "red rings".?

My fianc�e bought me a modded Xbox 360 Elite for a birthday/Christmas gift. Nothing was wrong with the package when it arrived, but after playing the Xbox for a couple days it began to go down hill so to speak. The Xbox would turn on in the middle of the night, open by itself and turn off by itself in the midst of a game. The Microsoft warranty is voided and the person I bought it off of on eBAY will not corporate with me at all. I know that I'm screwed out of my money with this but I would like to try and fix it myself with any help I can get here. I own all the tools to open the 360, and I am somewhat familiar with the internal workings of the Xbox. (I clean out my Xbox regularly and have modded my own controller.)