My DSi is broken and Im having issues getting Nintendo to fix it?

You should probably call Nintendo up and ask them why they sent it back to you still broken, and as for the whole picture issue i don't see how fixing the screen would cause them to wipe your memory, so i would not worry about that. But in case i'm wrong then while you have Nintendo on the phone still, ask them would them fixing the screen effect your memory. Hope you get everything fixed up soon!