Notebook Hardware and Upgrade Questions

The right hinge recently broke/stopped functioning on Pavilion laptop, where it is stuck in the upright position.  I am under extended warranty for pickup/return, but the 1st box sent to me from HP was already lost by fedex.  Mailing a laptop in the upright position could result in more damage and seems impossible at this point, along with the risk of fedex losing the laptop.  I plan to pursue a repair at an authorized repair center, but HP could not confirm if I would be charged by the 3rd party site, or if HP would cover the expense, since I am still under warranty.  It seems odd that HP cannot answer this and it is not clear why HP would not "cover" this repair by a 3rd party, when it is already been approved as a "repair under warranty".  Has anyone else experienced something like this with their care pack warranty?  It sounds like the hinges are a common defect on various models and very disappointed that is broke in my 2nd year of this laptop.  Thank you!