I didn't read anything except for Matt's last post...
The power led directly correlates with the drive status.
There's a wire on the DVD cable that has either 3v3 running through it (closed) or 0v (open).
My guess is that the problem is that wire is dead and is staying at 0v which means the 360 keeps the drive tray open (the drive itself opens the tray when that line is 0v).
I think the 360's eject button (based on how the drive acts) is a NC Tact switch. That is, the 3v3 is always connected to the drive and when it's cut (pressed) it triggers the opening. That depends on if the button is directly wired to the DVD drive connector.
It could also be a grounded switch which triggers it.
I'm too tired to think about this right now, but would there be a simple way of wiring up the eject button and DVD connector so that there's 3v3 running to the drive and then when the button is pressed, it cuts it?
This would mimic how the drive works, and since it looks like the 3v3 line is dead on the connector, this should effectively fix the problem.
Any thoughts?