You yourself contradict your statement. As you say even if you have those things that do not exist today or cannot be produced in the future, you probably couldn't go back in time any further than the instant the machine was turned on. I appreciate you keeping an open mind about this. But for now or in the future (theoritically), it is impossible for anything that has inertial mass to travel at the speed of light. But only with those with mass can measure time. Photons or radio waves has no inertia and they travel at a velocity that is equal to c. Time is insignificant for these as they do not travel at a velocity other than c. You need an inertial reference frame to measure the time it travels that simply do not exist.
Why do you find my statement contradictory? If you were able to use negative mass or energy to make a worm hole to create a time machine you couldn't travel back any further than the instant the machine was turned on? Is this the statement you mean? This is why time travel wouldn't be as much fun as most people would think. As long as the machine exists you could travel back and forth through that time period. Most people think of seeing the dinosaurs or watching ancient history but unless your machine was built before those time periods you couldn't go back that far. As for faster than light, you do have a point, you cannot, through what we would call normal means, accelerate a material object to or faster than the speed of light. But if you create an isolated pocket of space/time around your vessel and then expand space behind the space/time pocket and compress it ahead or your space/time pocket you could accelerate to any speed you wanted without breaking the universal speed limit (Alcubierre drive - Wikipedia, the free encyclopedia), while this is a theoretical way to go faster than light it is still far beyond even knowing if the engineering can be done or not much less doing it. Then of course you have worm holes which are just as difficult to make and use. Heim theory suggests it might be a little bit easier but it is still an unconfirmed theory. (Take a leap into hyperspace - fundamentals - 05 January 2006 - New Scientist) While none of these things can be used or even known if they could ever be used they do point out that the speed of light may one day be, if not broken then at least cheated.