Here's the deal:
My 360 won't stay on for more than 1 second.
That's it. Checked connections. Internal and external.
I need help because my warranty is void and I can't send it in to Microsuck.
If your friend is not the sharing / lending type, simply bring your console to his place to test it.
Used 360 power bricks really aren't that expensive these days, especially on eBay. ($25-$35 USD ... cheaper than investing in a new system if your brick is the sole issue.)
that happened to me too, it turned out to be that the wire wasn't stuck all the way in the brick's slot. You know the wire that can be taken out....stick it in good, then try it again.