The layer must be 3D and placed next to the text layer in 3D space. Simple as that. You don't use parenting. Only the camera should move. I am guessing you tried to position your pre-comp by just looking at it visually. Just copy the position of you text layer by setting a single position keyframe, then past it to your Pre-comp, then adjust the scale and position carefully.
This works best if you have set a ground plane and origin.
If the animation is a pre-comp then it is easiest to just make the pre-comp 3D. If the Pre-comp is made entirely of 3D elements then you will have to collapse transformations so the Camera in the main comp is used and the position of the elements will have to be adjusted so that it is close to the 3D text in the main comp. This is no different than using 3D pre-comps in any 3D project in AE.
If you still need help I'll take a look at the project.
I got it to work now by parenting the position of the precomp to the position of the null I made. Dont really understand why It didnt work before though. I understand now that what you mean with the one keyframe on the textlayer, I couldnt parent it because there was no data stored there.
Thank you for the response!
Just parenting a 2d layer to a 3D null may appear to work, but it really doesn't. I opened up your comp and all you have to do is to copy the position of the Text layer, turn the pre-comp into a 3D layer, paste the position of the text layer to the pre-comp position, scale up the pre-comp so that it fills the TV screen and slide it a little to the left. You have to scale it up because it's about 6800 pixels away from the camera. The pre-comp as a 3D layer would be the same size as the pre-comp as a 2D layer if the distance from the camera for the 3D layer was 796 pixels (the zoom value of the camera).
The reason it jumps around wildly as a 3D layer is that the Z position of the pre-comp is 0 and the z position the text layer is 6026.2. The text is where it should be in 3D space, the pre-comp isn't even close.
Now the pre-comp is in the same 3D space as the text layer and the whole thing will move as if it was actually in the scene.
Just parenting to the null will only kind of make it look kind of like the image is actually on the tv set. The perspective and parallax will not match.
Here are the settings:
Here is the comp (CS6) without footage, but you already have that.