I had a launchtime 60gb model. About a couple of months ago it started doing the cutting off randomly thing too. I never noticed any yellow lights though. Luckily about a couple of months before that I invested in a "just in case" brand new slim that had 3.55 on it. That slim was some good forward thinking for me, because the old one is now just spare parts. After opening it up, I saw an area on the motherboard that had taken some serious heat damage. Some kind of coating had even melting and leaked around onto the board in a certain corner. And in that area there were about 3 little electrical parts that looked burned to hell. My guess is that the second it needs to access that area of the board, it dies.
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