Alienware Laptop warrantee refused.

My Alienware m17x has a moth of warrantee left on it. The tech diagnosed it with 2 bad cores. there may also be an issue with video ad it sometimes get a blue line across the screen even in the bios. However Dell says there is accidental damage and will not honor the warrantee. The Damage being that the piece of plastic above the sd card is broken. It is broken as this is the point where you naturally hold the laptop when picking it up. The piece is an inch long and a quarter inch think. Because this is broken they want me to pay $180 to fix the computer. How is a broken piece of plastic case affecting the cpu cores and video?? Does this seem right?