If you have the tools, try removing the battery, and running it with just the AC adapter connected.
My wife bought me a "refurbished" DS lite and mailed it to me at my deployed location. She powered on the DS and said that it worked but when I received it, it didn't work. I plugged it in to charge and got the amber light as it should, but when I opened the system to power it on the amber light went off. So I removed the charger and plugged it back in and got the amber light back. When trying to power the system on without the charger connected still no power. Anybody know what the issue could be?

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