Can internal links from a blog harm the ranking of a page?
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Here is the situation: A site was moved from its original domain to its new domain, and at the same time, the external wordpress.com blog was moved to a subdirectory, making it an onsite blog. The two pages that rank the highest on the site have virtually no links from the blog and no external links, while all the other pages are linked extensively from the blog and have backlinks. Their targeted keywords are not so much easier to rank than the other pages for that to be the sole cause.
To confuse the matter even more, there was a manual penalty affecting incoming links which was removed last month. The old site, which has many backlinks to the new site, is still in Google's index. The old blog however, has been redirected page by page and is not in Google's index. Most of the blog posts are short 1-paragraph company updates and potentially considered low quality content because of that (?)
The common denominator among the two highest ranked pages (I'm talking top 3 in SERP v. page 3 or 4) seems to be either the lack of external backlinks or the lack of internal links from the blog. Could there be an issue with the blog such that internal links from it are detrimental rather than helpful?
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OK I think I understand what you did

"The old site, which has many backlinks to the new site, is still in Google's index"
So you are pointing links from a penalized site to your new clean site, hope you are using nofollows? hmmm. Not a good idea if not!I would not 301 redirect either. As this will simply assign all the bad stuff over to your new domain as well.
The blog is internal which is a good thing now, but the low quality will effect the whole site eventually. Low quality content must be addressed or Google will hit the site hard with the Panda Algorithm. That low quality then links to your internal pages, not a good idea either.
If the blog offers no real value and you are unable to maintain it then remove it for now completely and focus on creating a well rounded good quality site first. A few good blog posts is better than a hundred terrible ones.