I am assuming you have removed the clear plastic battery-insulator sheet from in the remote, and a CR2025 battery is in the ML-L3 remote, and the battery is in the battery tray with the plus sign facing up, and the battery tray is correctly inserted all the way into the remote . You can verify that the remote is working by putting your camera in liveview mode, point your remote toward the camera lens and keep pressing the button on the remote. While doing this in a dark area, you should see a purple light on your camera screen emitting from the remote.
The D3200 has to be in remote shutter release mode before the ML-L3 can be use with it.
(1)While in shooting mode, press the I-button (information edit button : the button at the bottom left of the D3200 LCD) to bring up the information edit screen. Your LCD will turn dark grey.
(2)Using your multi selector (Arrow buttons: up,down,left, and right), highlight the item located in the 4th column on the far right of the screen, and press OK. At default camera settings. you will see S. See page 31 of the user manual.
(3) Scroll down and select Quick response remote, or Delay 2 seconds remote, and then try using the remote.
D3200 PDF manual link:http://support.nikonusa.com/app/ans...
If the issue persists, technical support contact information can be found at support.nikonusa.com