So I've been doing the animation that will be seen on the TV and where the objects that fly out start from. To do this, I created a seperate scene from which I animated it as usual. I then rendered it out and brought it into After Effects to create an 'old TV broadcasting look'.
Raw Rendered footage:
Old TV broadcasting look:
I've now converted the video to an image sequence so I can use the Movie Node in Maya to display the TV screen and animate from there.