No DS card inserted and There is no gamepak inserted error messages on Nintendo DS

Problem Solved: Look into the socket where the cartridge is inserted and count the number of pins you see.
If it is less than 17, then you have a contact pin that has broken off or is bent to the point it can no longer be seen and is not making contact with the cartridge.
If you have warranty, take it back and have them replace the unit, if you don't have warranty you have to take the unit apart and replace the socket yourself. (WARRNING) if you have no experience with soldering, do not attempt this!
I have 30+ years in electronics and have taken these units apart, and have always found pins missing or bent over to the point of not making contact.
Hope this helps!