RE: XPS15z L511z won't boot (blank screen ) and beep at any key stroke.
Thank you for the update.
Find the link for the beep codes and error messages - http://dell.to/1NAsADX
Read the Notes in Yellow for a better understanding of the beeps and how to identify the source of the issue.
If you have diagnosed the video card to have failed and the motherboard to be replaced, we could help with a paid service call if required or you could contact Dell 3rd party parts seller - http://www.parts-people.com/and order the parts through them.
Let us know if you have any other queries.