It looks like the hinges, which should be easy to find searching "xps l501x hinge".
I can't quite tell from the pictures, but many times, the point of failure is the plastics behind where the hinges actually screw in. If that's the case, you'll need to replace the LCD Cover as well.http://www.ebay.com/sch/i.html?_trksid=p5197.m570.l1313&_nkw=xps+l501x+hinge&_sacat=0&_from=R40
If you've never taken a laptop screen apart before, I'd suggest a local computer shop. However, it can be done at home with some patience and the right tools. If you think you'll do more damage than you fix, take it to a professional