Question: When I consider my own existence with respect to time I can imagine three possibilities: 

(1) **Time extends infinitely into the past.** In this case, how can the present, with me in it, exist, since there would be an infinite period of time that existed before the present. That seems illogical. 

(2) **Time had a starting point from which everything in our universe evolved to the present (t=1).** That possibility would require something (God) to start the clock ticking (t=0). But in this case we're back to square 1 with the problem of an infinite past. So the only possibility that makes sense to me is a third possibility 

(3) **Where time is some sort of abstraction in human consciousness that we need in order to relate cause and effect.**

Answer: 
You've presented a false dichotomy: just because something is a "mental construct" doesn't mean that it can't also be a real property of the physical universe.

Take length as an example. "Length," as such, doesn't exist physically. It's not something you can see or touch. Nevertheless, it is a real quality of physical objects--it exists "out there" and not just in our heads. In this respect, length is like any other *measure*--it's an abstraction in the sense that it does not exist in and of itself, but it nevertheless describes real qualities of physical objects.

Time is no different. The more you understand of physics, the less sense it makes to think of time "extending" in any direction. Time isn't a medium, it's a *measure*, and what it measures is **change.** As for what change itself is, well...that's still an [unanswered question!](http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics)
3 is correct. Time is a abstraction, a filing system used to arrange events and memories into a logical system of cause and effect.

Per relativity, space and time are not discrete entities, but a single construct called spacetime. Saying something is X km long is equal to saying it is Y seconds long. All units of time are based on and can be reduced to measures of distance.

Time is a mental construct used to make sense of movement. Movement produces the sensation and experience of time, not the other way around.