Xbox 360 Controller to Nintendo 64 Console
The xbox controller is a composite USB device, consisting of a USB Hub, a USB HID device, and a memory device or two for the memory cards (or other accessories). Before the driver even begins to take control, the USB Host (I.e. the computer) must initiate a standard usb enumeration process.

If you plug in the controller to power, but the usb D+ and D- are left floating, it does not see any enumeration and shuts down. Like if you plug it into a dumb charger. Enumeration is typically expected to take place in milliseconds, which is why you only see it on for a third of a second (330 milliseconds, an eternity to a microcontroller).