Problem with my new (refurbished) Canon Rebel t4i. Anyone know what's going on?

Question

So, my girlfriend got me this sweet Rebel t4i for Christmas. I'm still learning how to use it, but it's giving me a problem, and I don't know if it's because something's wrong with the camera, or if I'm doing something wrong.
85% of the time, when I try to take a picture or video, instead of taking the picture, it just says "BUSY" on the screen. Sometimes the flash buzzes and flashes light, but no picture. Sometimes if I hold the button down for an extended period of time it will take a picture, sometimes it just fritzs out.
I really like this camera but because of my schedule I haven't found time to sit down and really figure it out. There's a warranty on the camera, plus it was purchased recently, so I need to know if I need to send it back.
I can take a video of what it's doing if that'll help.

Answer 1

There may be nothing wrong at all... this sounds like the camera isn't able to focus.  If there isn't much light on your subject (e.g. shooting indoors) and the subject doesn't have enough contrast in poor lighting, then the issue would be normal and not a camera problem at all.
By default, the camera is in "One Shot" mode -- but a side-effect of One Shot mode is that the camera uses a behavior called "Focus Priority".  
Focus Priority says that the camera is told NOT to take a photo UNTIL it can confirm that it was able to lock focus on something.   Depending on the available light, the camera may struggle to do this.  There must be enough light.  
But the camera has one more trick up it's sleeve... it can use the flash as a kind of focus-assist light.  It pulses the flash rapidly (which will making a buzzing sound) in order to add enough light to the scene so that the camera can hopefully lock focus.
Once it can lock focus, it's happy to shoot.  
If you switch the lens to manual focus (set the "AF/MF" switch on the side of your lens to the "MF" position -- that's Manual Focus), THEN the camera is told that YOU are taking care of focus and to just shoot whenever you press the shutter button (there will be no delay -- of course the camera wont even attempt to focus.)
For action photography, you can put the camera into "AI Servo" mode which continuously tracks focus on a moving subject.  But a side-effect of AI Servo mode is that the camera uses "Release Priority" behavior instead of "Focus Priority" behavior.  In this mode, the camera is told to take the shot as soon as you fully press the shutter release (hence the name) and it will do so EVEN if the camera did not finish focusing (normally you'd half-press the shutter and wait for it to focus -- you can also configure a back-button to focus as well.)
Take your camera outside during the day and try shooting when you KNOW there is plenty of light.  It should have no problem.  Inside... it needs enough light.
Canon's 430EX II speedlight flash has a red focus-assist beam built into the flash.  When you use that flash it will use the focus-assist beam on the flash to focus the camera (the flash projects the beam through a red lens in the lower part of the flash -- and the camera is able to lock focus on the pattern being projected by the beam.)  You can even use the flash to create the focus assist beam EVEN if you don't want to use flash (you can tell the camera to disable the flash -- in which case it will just use the beam but wont fire the flash.)
Hope this helps!
Regards,
Tim
Tim Campbell
5D II, 5D III, 60Da