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The best links are the ones that your competiors don't have and aren't going to get. That means that backlink analysis is not much use in uncovering them (other than maybe for inspiration). Tools like OSE (or majestic seo / ahrefs ) can be useful in picking up low hanging fruit.  However it seems to be the big ripe juicy fruit further up the tree that makes a difference at the moment. The best tools for finding those are Google + Inspiration.

Even though there are less pages indexed compared to those that are blocked, you still have a significant increase in indexed pages as well.  That is a good thing!  You technically have more pages that are indexed than before.   It looks like you possibly relaunched the site or something?  More pages blocked could be an indexing problem, or it might be a good thing - it all depends on what pages are being blocked. If you relaunched the site and used this great new whiz-bang CMS that created an online catalog that gave your users 54 ways to sort your product catalog, then the number of "pages" could increase with each sort.  Just imagine, sort your widgets by color, or by size or by price, or by price and size, or by size and color, or by color and price - you get the idea.  Very quickly you have a bunch of duplicate pages of a single page.  If your SEO was on his or her toes, they would account for this using a canonical approach or possibly a meta noindex or changing the robots.txt etc.  That would be good as you are not going to confuse Google with all the different versions of the same page. Ultimately, Shailendra has the approach that you need to take.  Look in robots.txt, look at the code on your pages.  What happened around 5/26/2013?  All those things need to be looked at to try and answer your question.

Have you run any campaigns on FB, Twitter G+ for the page you want to rank? No. we just have company pages on the social networks

Thank you very much for your advices. Really helped me out here. I will message you sooner or later and tell you how it went, if you are interested. This week I will make a presentation for the team with the reports. I think this should be addressed ASAP