Edit >> Preferences>> General (tab)
Lightroom >> Preferences>> General (tab) on Mac OSX
Check the box: Show import dialog when memory card detected.
The SHOW IMPORT DIALOG WHEN MEMORY CARD DETECTED has been checked off but Lr still doesn't open automatically.
Could be a hardware problem. Do you have a separate card reader to try or a card slot on your computer.
Try formatting the card inside the camera before taking more photos. Formatting the card inside the camera is the best way to tell LR that this is indeed a camera card and not just another memory storage device.