I would try something else too, try plug in the usb cable and running the flash wizard till it gets to that point where it wants to find a device then plug in the usb and then the power while holding the home button.
I don't know if it will do anything but it might get you to a new step and you might get it to stay on after that. I have had the same problem as you before, I left the battery out over night and replaced it in the morning and it came back on.