The popping, can you tell if it's your speakers or not?
If not, it may be the sound of something like a circuit relay popping.
If so, if you're good with soldering then you could open up your DS and feel of each chip to find which one it is.
I've not opened up and looked at a DS, so I wouldn't know for sure.
I googled it, but couldn't find any schematics on it's circuitry.
You should be able to feel the pop on whatever chip it is.
That being said, there are other possibilities to try before hand.
Perhaps your battery could be sending too much power to the DS, and it's popping once heated up to a certain point?
That's just a thought.
So try another battery? If it's a phat DS, the GBA SP's battery will work in it.
If another battery doesn't work, then I'd personally just sell it as is on eBay and buy a new one. :3