I haven't personally witnessed this myself, but usually the first thing to suspect is bad polarizing film. you can purchase replacements, but not cheap. the adhesive is probably degrading causing the issue. in RARE cases, the actual liquid crystal is going bad, although the liquid crystal if pure does NOT degrade. only if there are impurities in place.

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The symptoms are hard to reconcile with the "bad polarizing film" theory. The darkening worsens as the thing operates. But if you turn off the computer and let it sit, the LCD often looks fine the next time you turn it on, and then degrades again over a tens-of-minutes time frame (typically). In the corners. By a process of Holmesian winnowing, one is led inevitably to conclude that it is in fact the liquid crystal itself. LCs are quite easily poisoned by water. Indeed early LCD work was frustrated by the difficulty associated with removing all sources of water (both initially, and from chemical reactions that liberate small amounts of water over time). A famous story from the early days tells of RCA's woes when researchers ordered "medical grade" liquid crystals, thinking this would be the good stuff. It was full of water, and their displays had short lifetimes.