Very simple test...
1a. Set ISO 100 and 1/100 f/16 and take a JPG photo (assuming bright sun), or
1b. Set ISO 100 and 1/100 f/4 and take a JPG photo (assuming heavy overcast)
2. Remove memory card from camera. Put it into card reader on PC, open the photo file,
2a. if you see a full scene the shutter is working just fine, and the camera is writing the JPG properly to the memory card.
2b. if the photo is screwed up, your data is not being written to the memory card properly by the camera
If 2b, try a different memory card and repeat the test.
If 2a, put the memory card back in the camera and try to look at the photo on your LCD. If you cannot successfully see the same photo on the camera that you saw previously (2a) in the PC, your camera is in need of repair.