If runny colours or blotchy colours permanently remain on the screen, even when the Nintendo DSi is OFF, then the liquid crystal display (LCD) is cracked.
This malfunction can only arise from an external event, e.g. the device being placed under stress or subjected to impact.
Breakage of the LCD is a fault that can occur only as a result of an external influence. Such external influences are the result of improper handling of devices, accessories or games. In this case, the warranty becomes void and repair charges will apply.
To correct this issue the Nintendo DSi will need to be returned to Nintendo Australia for inspection/repair.