I'm trying to figure out how to begin writing a piece of code that listens for user activity. If there is absolutely no activity after a few minutes I want the game to restart. Can someone recommend a good starting point to get something like this working?
If you are wondering how to capture all input from everywhere, take a look at
Input.anyKeyDown
http://docs.unity3d.com/ScriptReference/Input-anyKeyDown.html
In addition you can also check that the mouse position is still the same as the previous frame. Use this in combination with @Neeraj Kumar's answer i.e.
private Vector3 prevMousePosition = Vector3.zero;
void Update()
{
if(Input.anyKeyDown || Input.mousePosition != prevMousePosition)
RestartGameInvoke();
prevMousePosition = Input.mousePosition;
}