I didn't know that a screen can become completely inverted after it was dropped on the floor, but well, I just hope that this never happens to me. Nevertheless, the solution can either be to use compiz and invert everything or you can just use xcalib with the -invert switch. This switch I've added just for fun because I wanted to see whether it's possible to set arbitrary values in the video LUT. The interesting observation there was that X11 does not check the values, whereas on Windows the operating system does not allow you to set completely unlikely screen calibration values. Hence, this will only work on Linux:
xcalib -invert -alter
When you are going to do color-critical work (which I don't recommend with a knowingly broken screen!) and wanto to create an ICC profile, be careful: many calibration tools reset the LUT to the default values (the equivalent of xcalib -clear) - which are totally useless in this case to derive an ICC profile. Hence, better explicitly disable screen calibration in this case!