Dig out the user manual and follow the instructions for doing a full camera reset. If you have a lighted magnifier look deep into the card slot and make sure it's free of debris, dust bunnies or flotsam.
From there, if it still isn't responding, try reformatting your SD cards. First, save copies of any irreplaceable image files from your SD cards before reformatting. If you can't reformat in-camera, try first reformatting in a desktop or laptop PC assuming you have available memory card slots or a card reader.
If the camera now recognizes the SD cards you might as well format them again in the camera to put everything as right as possible. There is also a very tiny switch on the door that covers the SD card slot (as well as the battery door) that tells the camera when the door is fully closed. Unless it doesn't, in which case it will not let things work as expected.
Exactly what brand and model and capacity of SD cards are you using? How old or heavily used are they? Are they full sized SD cards or Micro SD cards used with an adapter?
