If you wanted to approach this question as a pure Heideggerian, it would be a matter of deciding whether a new epoch of being has overtaken us, determined by some change in our relationship to technology, or whether we are still immersed in the same epoch described by Heidegger. He describes modern technology as completely determining the possibilities of Dasein, so that we see ourselves as set forth by technology, rather than vice versa. If you understand us as continuing within this epoch, then the possibility of salvation (so to speak) still remains in recognizing the essence of technology.
If you prefer the theory that our technology has opened a new epoch, then you could take these reflections in any number of directions. I believe that Bernard Stiegler has developed a philosophical project along these lines - you might take a look at Technics and Time, 1: The Fault of Epimetheus.
My own preference is for Derrida's response to this direction (or Weg) of thinking. Derrida questions the possibility of distinguishing authentic from inauthentic thinking, and thus deconstructs the oppositions between animal or technological existence and that of Dasein as they are developed by Heidegger. You can take a look at Derrida's Of Spirit: Heidegger and the Question or "The Pit and the Pyramid: Introduction to Hegel's Semiology" (In Margins - of Philosophy for more on how the deconstruction of authenticity and inauthenticity leads to a questioning of the distinction between Dasein and mechanical thinking.
One way to think about how deconstruction can change our thinking about our relationship to technology is to consider what it is that we are trying to get away from when we try with Heidegger to disclose a thinking that is not technological. Derrida would argue that the possibility for technology, which is the possibility for any sort of prosthesis that extends or alters our "natural" capacities - of voice, reach, or physical power, for example, is not something that comes along after the fact to affect a subject who is completely self-contained and authentic, but rather an extension of the difference-from-self that is already present in all of our self-relations, including thought. This or that technology may change our relation-to-self, but never in the essential way that would transform a self-present (authentic) subject into an absent-from-self or inauthentic one. Of course, according to Heidegger we are always falling away from authenticity, and requiring an effort to arrive back at an authentic relation to our own possibilities for being. But I would like to question the extent to which "technology" is a force preventing our return to authenticity. It may be that there is still something technological, technical, something of technique that is still a part of even the most "authentic" thinking.
The developments of mechanical and computer processes that increasingly resemble human thought should also lead us to pose the question whether or not authenticity and/or inauthenticity are possible for machines, that is, for technology unto itself.