I just bought a piece of cleaning cloth made by 3M. It's a 'microfiber' computer cleaning cloth, and it has cleaned off most of the dust and small oily spots on my beautiful glossy laptop screen (a Sager 8790 screen) WITHOUT even using any cleaning fluids.
My advice is, get one of these reusable cloths, and make your own cleaning solution. I haven't tested it yet on my laptop screen, but most 'cleaning fluids' they sell are just some kind of alcohol and water mixed. You could probably do this yourself with a 50 cent bottle of rubbing alcohol from a drugstore (for disinfecting wounds) and diluting it with clean filtered bottled water, then spray a tiny bit on the cloth before wiping the screen. That, I think, would get rid of the most persistent dried stains.
Again, I havent yet done this so I can't guarantee it, but you can verify the accuracy of what I've said by looking at a bottle of normal computer cleaning fluid. Usually an alcohol and water.
One thing they always say is never to spray it directly on the screen. It's too easy to drip down and into cracks. Water and laptop components don't mix.