Nintendo will fix it for free. The thread is a bit old, but you should call Nintendo support and ask. https://www.engadget.com/2006/07/21/nint...-fesses-up-to-ds-lite-hinge-defect-will-fix-for-free/
If the game isn’t working, try to shove a thin piece of cardboard or perhaps even a clothing tag in along with the game. It worked for my original DS, which I got for free because the game wasn’t showing up when the system turned on. Note that this seems like a horrible option, but it honestly worked for me after a few tries and putting the game in a certain position in the game slot. Also note that this was an ORIGINAL ds system, so it may not work for a 3DS, but if all else fails, try this BEFORE attempting to take the ds apart!!
If the game isn’t working, try to shove a thin piece of cardboard or perhaps even a clothing tag in along with the game. It worked for my original DS, which I got for free because the game wasn’t showing up when the system turned on. Note that this seems like a horrible option, but it honestly worked for me after a few tries and putting the game in a certain position in the game slot. Also note that this was an ORIGINAL ds system, so it may not work for a 3DS, but if all else fails, try this BEFORE attempting to take the ds apart!!