1.) Only games you downloaded via nintendo Eshop transfer with an SD Card. Physical cartridges need to be manually moved throughout 2DS's
2.) Take it to your local GameStop or EB Games, etc. See if they know anything about this
3.) Maybe it has something to do with the fact that your previous 2DS was broken. Perhaps your broken 2DS corrupted the SD card somehow
4.) Take out the SD Card, blow on it, clean it, and put it back in. Pretty simple.
5.) Let your 2DS die, and then try again. You could also turn the 2DS on and off but it seems to work better when you let your battery run out. I tried this after my 3DS screen kept flickering when I spilled water on it.
That's all I can think of and good luck. I know firsthand how stressful it is to find your Pokemon data unresponsive