Why does my Asus laptop screen go black when unplugged?

Asus N61JQ laptop screen turns off upon unplugging power cord

I'm running Windows 10 64-bit on my ASUS N61JQ laptop. Immediately upon unplugging the power cord, the screen on the laptop turns off. Battery is at 100% charge. With a second monitor attached, the second monitor is unaffected and stays on. Power plan settings say: On battery power, turn off after 10 minutes. I've tried setting this to Never, but it makes no difference. When I say the screen "turns off," I don't mean that it's a blank screen with some backlight. I mean the screen looks the same as if I totally shut down the system and turn everything off.

Also, ever since upgrading to Windows 10, I can no longer change the brightness on the display. Sliding the brightness bar down from 100% changes nothing, until it gets to around 60%, at which point the laptop display turns off completely, just like it does when I unplug the power cord. Putting the power cord back in or sliding the brightness bar back above ~60%, as the case may be, causes the display to immediately turn back on.

Neither of these things was ever an issue for my laptop with Windows 7 installed. The video card is an ATI Radeon HD 5730. Until this evening, I had the most recent video drivers installed. Through Control Panel, I went to the properties of the video card and told Windows to look for new drivers. It found them automatically and installed them. No change to black screen problem.

Any ideas or possible solutions would be greatly appreciated