When you are taking a picture at low ISO in the dark, even with a relatively wide aperture (f/3? Are you sure? That's an odd number not normally used in the sequence), the shutter speed is going to be very long — possibly several seconds.
The sport mode probably cranks the ISO way up to prevent this.
So, that's one thing. And you are probably not using a tripod, so it's going to be impossible to get a sharp image, because you just can't hold the camera still for more than a small fraction of second, even if you have very steady hands.
Then, the next thing that happens is that the camera is automatically enabling dark frame subtraction. This helps cancel out noise by taking a second exposure of the same length but with the shutter closed, and then canceling out anything that appears (because it must just be noise from the sensor, not light from the actual scene). That's why your camera isn't responsive immediately.
On the D3200, this happens automatically when your shutter speed is 1 second or longer. See page 131 in the manual; the exact conditions vary based on sensor temperature (hotter is worse) and it kicks in sooner at high ISO (but low ISO may require a longer shutter speed, so it will kick in anyway). You will see Job nr, for "Job noise reduction" in the viewfinder while this happens.
On some cameras, you can disable this. On the D3200, you can set NR to "Off", but this really means "less", not actually off, and I'm not sure offhand if this disables dark-frame subtraction. Unless you are manually taking a dark frame and using it in your RAW conversion software, you probably actually want it anyway.
