If it were to get damaged in shipping, the only way you'd have a successful claim against the shipping co is if you did the following:
Pack the monitor (preferably in its original box) in a box only slightly larger than the montior itself. Provide adequate padding/styrofoam inside that box so that the monitor does not shift around. When you get done with this box you should feel like "yeah I might be able to ship it like this..."
Now place THAT box inside another box which is at least 4" bigger in all dimensions. You must pack it with 2" of styrofoam peanuts (or equivalent) on all sides.
If you're shipping out something as $$ and fragile as a LCD monitor, save yourself the risk of having it arrive destroyed and pack it correctly. You can buy big bags of styrofoam peanuts at places like office depot, or if you really want to get screwed, pack and ship places.
Crumpled up newspaper isn't really a very good packing material. Styrofoam or foam-rubber is a much better choice. Bubble wrap is also good.