get some alcohol and a q-tip, clean the scratch as well as you can get all the dust and crap...loose pieces out of the way first. get yourself some clear 2 part epoxy. mix it up and apply it to the scratch inside the vally of the scratch. let it rise out of the scratch somewhat above the level of the glass. before it dry's take a metal putty knife or a box knife razor and scrape off the excess epoxy from the top of the glass. when it dry's it should be alot better than a deep scratch, and if your lucky, looking at it from a dead on angle you may not even notice it.
second option.....take the monitor outside and blast the crap out of it with your favorite gun, invite some friends, cook some dogs, make it an occasion. Make sure you've got a sutable replacement before proceding with option number 2 though....