Oh man! I have pretty much ALMOST the exact same problem.
My neighbor sent over his DS to my place so I can repair it.
It wouldn't turn on.
And when I plug it into any charger using any socket, the orange light would only come for half a second then disappear.
I tried using the same charger for other DS lites, worked fine.
I thought maybe... battery issue?
I swapped its battery with my old DS lite's battery.
And now it makes orange light completely when we charge it.
That really got our hopes up.
Fully charged it, and then we pushed the slider to turn it on...
Snap! It wouldn't turn on.
So now my neighbors DS lite is exactly like yours, but I have a pretty good power switch.
I'm gonna send it to one of my personal favorite stores. (Geekay Games)
And this is also why I despise eBay.
I GOT A FAKE POKEMON FIRE RED AND LEAF GREEN GAME DAMMIT THEY KEEP RESETTING AND HAVE UGLY FAKE STICKERS.
They should like make a new emoticon in GBAtemp. Like, :yayamazon: