DS Lite won't power on after initial setup?

When I try to turn the DS on to set it up, it powers on fine, and works great. But when I try to turn it on after that, nothing. I can reset it by trying to turn it on without the battery, put the battery back in, turn it on again, just to repeat the process.

I also experienced this problem some before I replaced the touchscreen, but it was irregular. It seemed to be working after the replacement, yesterday I was playing a game and it was working great. Now it's having this weird issue.

I've kept it on the charger a long time, and swapped with a battery I knew was good, nothing.