An E69 error with an Xbox 360 console (on boot) indicates a problem with the hardware connected to the unit. The dark on-screen message directs a user to contact Microsoft Customer Support with details of the error, where it may be covered under warranty. At the same time, a single blinking red light will be noticeable in section 4 of the ring of light at the front of the Xbox 360 console.
An E69 error, like an E67 error (and to a lesser degree, an E68 error) indicates a problem with the hard disk drive connected to the unit. Information that has been gathered online about this problem from users shows that it may be associated with the Xbox 360 unit failing to read the HD Security Sector which is present on the Xbox 360 HDDs. It is possible that a disrupted connection with the drive would result in this error too.
To confirm it as a hard drive error, a user should remove the HDD bay from the top (or side - depending on whether your console lays flat or stands) of the unit and reboot. If the boot is successful without the hard drive, then it is confirmed as the problem. Getting this error while trying to use an unauthorized HDD that was flashed using a hack tool would indicate that the flash failed. In that case, it shouldn't cause any damage to the console that needs to be worried about.
An E69 error is associated with the error code 1011. To get an error code from an Xbox 360 console that is displaying an E69 error (or 3ROL) you simply press and hold the "sync up" button (used to connect wireless controllers) and then press the Eject button for the DVD drive. This will bring up the first digit of the error code (usually it is one light blinking red, which represents 1, please note that four lights blinking red represents a 0, not 4). With the sync up button still held, press the Eject button again and you get the second digit. Do this twice more to get the full 4 digits of the error code.
For more information on the error code you receive, or on Xbox 360 hardware problems in general, read this Xbox-Scene forum thread.