hi
I own a Canon 600D and I know I experience similar issues (not taking pictures when pressing the shutter button) with it as well.
What I do realize is if the camera is in MANUAL mode and the lens is in AUTO FOCUS mode, half press the shutter button long enough for the camera to focus on a subject (until you hear a short beep - if you configured the camera to make the sound once it has focused successfully) then press the shutter button after, It should take the shot.
Let me know if that works or if not.
You may also try the ff and see which one works:
[] reseating the SD card and the battery
[] changing modes to AV, TV, M, Automatic (A)
[] reseating the lens
[] updating the camera's firmware via Canon's website