ThinkPad T400 backlight doesn't always turn on when booting from battery

ThinkPad T400 backlight doesn't always turn on when booting from battery

I have a Lenovo ThinkPad T400, which I've owned for about a year. A while back, I noticed a problem in which the LED backlight would not always turn on when booting from battery. Usually, if I hold the power button down until the BIOS screen shows up, the backlight turns, but sometimes even that doesn't work. If I just press the power button and let it go right away, the backlight usually doesn't turn on.