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Well the content and the UI will change dramatically for the better.  The site looks ok now but it doesn't engage visitors.  The Blog still has the old UI but we're posting new content to the blog everyday and we'll put the new skin on the blog when the main site goes live.  So if I am reading your response correctly I could probably continue with building links related to the blog but should hold off on links to the main site.

One follow up question.  What are your thoughts one paying an SEO to do linkbuilding?  It seems that paid linking building is probably ok for getting a lot of links to lower ranking sites but sites that have a high domain authority will have to be manually done by someone in house.

We are in the process of completely rebuilding our web presence.  We went ahead and started a blog using Hubspot while we are redesigning everything and writing all new content.  The new site will be live in early August.  The question is when do we start making a big push with Linkbuilding?  I am currently trying to promote the Blog but I'm wondering about linkbuilding for the rest of the site?  Do we wait until the new site is live or do we start doing it now?  The new site will be completely different from the old site?