After Effects has no 3D tracker, it has a camera tracker. For Track Camera to work your shot needs fixed geometry in the scene and a fairly standard camera move. Your description of the shot you want to use does not say anything about camera movement.
Matching perspective on steady or locked down shots is usually easiest to handle with Corner Pin or Corner Pin tracking. The trick is that the Corner Pin effect uses the full layer size so you need to take that into consideration. Corner Pin tracking uses the frame size of the layer you are tracking.
With a little better explanation of what your camera shot is like we can point you in the right direction. If you want to explore options on your own and you are relatively familiar with AE then type corner pin or Track Camera into the search help; field at the top; right corner of AE and check out the community resources.
BTW, it's so easy to post images to this forum. you just have to drag them from the desktop or finder. Screenshots on windows are a simple matter of pressing Print Screen and then Ctrl/Cmnd + V (paste) in the forum's reply field. Referenced images from the internet can be added using the little icon at the top of the screen -
so in the future please add your images to your posts. It makes it easier for us to help you.
If the camera is not moving then your best option is to just apply Corner Pin to the replacement screen and then do some color grading. You might want to experiment with blend modes.