Actually though it's not exactly wrong, we managed to capture once a significant signal that could be of alien origin. It's called the wow signal and you can find more here: http://en.wikipedia.org/wiki/Wow_signal
The basis of the Fermi paradox though isn't about what we did/do to contact alien civilizations but the fact that even if one advanced existed in our galaxy they should have already found us even if we weren't looking for them. Which brings us back to the conclusion that there might not be advanced civilizations around and life could very well be in the beginning.
As for the Drake equation it's not a law of physics. It is just a way to estimate the number of habitable planets in the galaxy and from there to make an assumption of the number of alien civilizations able to make interstellar contact.
In other words, the equation was created to help guide research, not to answer the question itself directly. As a guide to research, I think the equation remains highly relevant.