There are a list of links pointing to my website that, for some reason, google and others have not found. Is it possible to make the search engines aware of these links in order to improve my placement on searches?
how do you know they haven't been found? google doesn't report all the links it has found. have you checked to see if the links have a nofollow attribute or if they are on pages that have a robots nofollow meta tag?
I used Google webmaster tools, and it reports that...
That is a sample. It does not show all links, it does not show all links that count, it does show links that do not count, for instance, nofollowed links. The backlink data Google provides can not be used to make assumptions about the algorithm- and that includes whether Google has found those links and is using them to calculate your rank.
I'm going to expand this because it's part of a larger issue This carries over to all Google searches. The data they provide is not SEO data. It cannot be used to make assumptions about the algorithm. This includes intitle, inurl searches. When those searches first came out this board was buzzing with discussions about why an intitle search shows their site as number one but not in the SERPs. Well, part of the answer is that the specialized search is just a specialized search and it was never intended to reveal anything about the algorithm that ranks a normal query.