Why are we blind for the era before the recombination? At recombination, Universe became transparent to electromagnetic radiation after universe expanded enough to cool down to form neutral atoms. Before that, the matter plasma was effectively opaque to electromagnetic radiation due to Thomson scattering by free electrons, as the mean free path each photon could travel before encountering an electron was very short.
This Thomson scattering is good to stop photons, but not Neutrinos. There are known Neutrino scatterings in theory, but it's probability is very low, AFAIK.
Why can't we detect neutrinos from before recombination era which can tell something more about initial phases of universe?
 A: You are perfectly right: neutrinos hold the promise of providing a window that gives us views much deeper into the big bang than the window conventionally provided by photons. 
The Hubble Space Telescope gives us snapshots of galaxies in a universe that is only 600 million years old. Although this feat is brought to the wider public as big news, the Hubble does not get anywhere near to exhausting the penetration depth of photons. The true capability of photons is provided by telescopes that observe at wavelengths much larger than that of visible light. The COBE, WMAP and Planck space telescopes all do so, and provide us with a view of the earliest universe accessible via photons: a universe that is only 380 thousand years old.  
With the universe at earlier times being opaque to light of any wavelength, we seem to have reached the limit of how deep we can probe into our past. 
Enter the neutrino. If we find practical ways to detect ultra low energy neutrinos, we will be able to dive much deeper than ever before into the big bang. Neutrinos hold the promise of opening a window to a universe that is only two seconds old. A prospect that will cause many a cosmologist to drool. 
Yet, the technical challenges are immense, and many believe mankind might never be able to observe directly such an extremely embryonic universe. However, we should keep in mind that neutrino astronomy is 25 years young and in its very infancy. Neutrino observations have reached a stage of maturity comparable to the maturity of photon astronomy at the time when Galileo for the first time pointed a telescope at the night sky. We have gone a long way since. The step from observing the first few extragalactic neutrinos twenty five years ago to the detailed observation of the Cosmic Neutrino Background, is probably not that much larger a step than the step from Galileo's first telescope to WMAP. 
A: Detecting cosmic neutrino background (~1.95K) is extremely difficult (compared with cosmic microwave background) and never performed directly so far. That's because neutrinos interacts with matter very weakly, unlike photons. We have to build very large detectors. (But if they behave like photons we can't use them to observe early universe.)
I also found quite useful introductory slides about this problem at lbl.gov:
http://www-physics.lbl.gov/seminars/old/Petr_Vogel.pdf
