Einstein a Go-Go

Ok, bear with the ignorant Earthling, but i've just watched the Science of Dr Who with Brian Cox. Very entertaining, but im not an astrophysicist, so one or two concepts escaped me. Following on from Woodsys diagram of the one shown on the show, which illustrated the passage of spacetime, Prof Cox showed a 'future light cone' and a 'past light cone' emanating from any given point in time, namely our present moment.

According to Einsteins Special Theory of Relativity, time travel is impossible, due to the inability to exceed the speed of light. Light travels in straight lines, at a fixed rate, but does it travel backwards in time ? My understanding of the theory is shown above, i'm sat at the centre, being me. My future extends before me and my past (naturally) sits behind my current timeline. Apparently, the light cone extends at 45 degrees to my present time plane, both into the future and back to the past. My understanding of light is that it proceeds in all directions, so should logically be a sphere, as shown on Wotans Special Theory, above.

If however, light (or spatial events) radiate outward, as Cox suggested with Faradays candle, infinitely, then light from a cone in the past, should therefore impinge on events in that points future (my present) as shown below.

So if light cones, or in my concept, spheres, extend forward and backward instantaneously, surely, time travel is occuring, contrary to Einsteins theory? If a past event does radiate forward, does it in any fashion effect the future event ? Apart from the actual causal chain of real events ?

or am I missing the point here......?