The backlight of the E63 is controlled by an ambient light sensor. This little glass dot to the right of the phones speaker determines how much light is available and adjusts the backlight accordingly. This is done to conserve battery power.
There may be times when the light is not enough, but the backlight won’t come on. To force the backlight to stay on, simply cover the ambient sensor on the right of the speaker with your finger as you type.
The backlight will remain on as long as you cover the sensor.