RE: XPS15z L511z won't boot (blank screen ) and beep at any key stroke.
The replacement battery on the machine, is that a Dell battery? Where did you purchase the battery from? Does the system power on and boot up with the adapter only? If you still possess the old battery, could you try booting the machine with the old battery?
Release the static power - remove the adapter and battery and press and hold the power button for 15 seconds and then try powering on the machine with the adapter only or the battery only and check if it comes on - download the service manual if required - http://dell.to/1QrXn0h
Please connect an external monitor and check if the display comes on. Try swiveling the laptop LCD and check if the display comes on.
Run the LCD test - turn off the system and press and hold the "D" key + power button to turn on the system and it should run the LCD built in self test - see this link for more info - http://dell.to/1SkXNrG
Run the diags - Press and hold the fn key and power button to turn on the system and see if the display comes on - or leave it for a while and check if any beeps in a cycle are heard. The exact# of beeps would isolate the source of the issue.
Keep us updated.