Help fixing my DSLite?

Problem description:
My DS suddenly powered off one day while I was playing. I tried to turn it on again but it wouldn't.
When I plugged in the charger the orange light turned on, so I assumed it was just out of battery. When it was fully charged (orange light turns off eventually), I turned it on and was able to get into the game normally (green light on) and play for about 20 seconds with both screens fine before it powered off again. When I immediately tried to turn it on again, it wouldn't turn on.
I've repeated this about 3 times just to check-
When charging, the orange light comes on.
After charging, I can turn on the DS and it works normally with green light and both screens for about 10 -20 seconds before dying.
After that, attempts to turn it on don't do anything until fully charged again.

Attempted Solutions:
All I've tried so far are charging it (as stated above) and replacing the battery. Neither of these has helped. I looked up common problems, and a lot of sites advise bridging the fuses. However, in the descriptions those DS's will just flash for 1 second before turning off, whereas mine functions normally for over 10 seconds before turning off.

What do you think might be the problem, and could you tell me/send me a link describing how to fix it?