The first thing I would check are how the Power Options are set up. These manage the power consumed by your laptop and it is possible they are configured in such a way that the display dims when the laptop is under battery power. You can find these by looking at the power settings in control panel.

A more serious possibility is that the LCD display has an issue. It could be a faulty backlight or a faulty inverter. The backlight is basically the light bulb in the laptop LCD screen. The inverter is a separate piece from the LCD screen. The inverter essentially takes the DC power converts it into AC power and steps-up the voltage to light up the cold cathode fluorescent backlight.

A dim display is often the result of a faulty inverter. This is very expensive to troubleshoot. The best way to determine the cause is by trying either a new LCD screen or a new inverter. Purchase an inverter first as inverters are less expensive than LCD screens. If the laptop is very old and infrequently used it might be less expensive to replace it, rather than repair it.