The older Xboxes & 360's can be finicky.
I have a 360 That I hadn't turned on in like 3-4 YEARS. Newer model.
Hit the power button, red light on the PSU. And RROD
Spent the better parts of two days and two "new" PSU's trying to reset / get it working.
What finally "fixed" it:
Blowing the "dust" out. Yep - not even stored it a dirty / dust area.
So if any gets an old 360 with a red PSU light - some tips:
Plug it strait into the wall, no power strips / filters (per Microsoft).
Disconnect Everything and reinstall - Try the original A/V connector with the HDMI unplugged.
Use some compressed air and blow the crap out - you may need to do this 2-3 times.
Try Holding down the eject button when powering on. I don't remember what specifically this does, but after the forth time I did it - success!
Hopefully this will save somebody some headaches down the road.