Send it back, accept no other solutions from them!
Say you wish to RMA (return merchandise authorization).
Say it was damaged in shipping and that the support have been less than helpful and that problems are getting worse, say that's it's unacceptable and your really disappointed by how your being treated by support who are gave you a quick fix for the screen that didn't address the actual damage done to the laptop.
Do not attempt to repair the PC yourself as HP may try to claim this removes warranty.