The screens of the Sony Vaio VGN-AR series laptops are a large 17", which inevitably makes the lid of the laptop quite heavy. The hinges cannot take the strain hence results in one, if not both of the hinges becoming weak and snapping. The only way to solve this is to exchange the whole broken hinge.

You can find the hinge here; http://www.sonyvaiopart.co.uk/index.php/sony-vaio-vgn-ar-17-left-hinge-with-small-holes.html