When the unit starts, you will see the Health and Safety warning and "Touch the Screen to Start."

In the menu, where the DS game should appear, it is ghosted out and says, "There is No DS Card Inserted."

First off, to remove the possibility that it is not something extremely simple and overlooked, try this: http://www.nintendo.com/consumer/repair/...

It might just need to be cleaned. this is the simplest starting point, and needs the least amount of tech. http://www.fixya.com/support/r4080144-ds...

Past that, you can try replacing the Slot-1 slot on the motherboard, replace the motherboard, or get a brand new unit. I do emphasize the cleaning first. Being a portable unit, it's in pockets, backpacks, greasy hands, who knows what... You get the picture.