One obvious way to fix this is to replace the display. I think you can get it for 10€/$ on various places.
I think this is a common problem of non-expensive displays (and even more expensive ones) -but especially annoying for cases, where the backlight comes from only one direction: the reason why unidirectional backlight does not look "uneven" from the beginning, is that there is a reflective and light-dispersing layer behind the TFT layer. This layer can change its dispersing effect over time due to mechanical and/or chemical processes (i.e. oxidation, slight deformation due to relaxation processes after production). On bigger screens this results in clouding effects and here this means this strong difference in brightness from left to right.