Hi,
I don't know if this is exactly a fix for your problem but it might be.
Here is a link which shows the replacement of the hinges in an Asus laptop. While it is not your model hopefully it is close enough to be relevant to yours so as to be useful.
https://www.youtube.com/watch?v=z8MxzocTnsY
Here is a link which shows the replacement part.
http://www.ebay.com.au/sch/i.html?_odkw=asus+n56vz+hinge+kit&_osacat=0&_from=R40&_trksid=p2045573.m570.l1313.TR0.TRC0.H0.Xasus+n56vz+hinges.TRS0&_nkw=asus+n56vz+hinges&_sacat=0
I hope this will be of some help to you.