The content of the page doesn't affect the weight given to a page's title. It just affects the weight given to the page as a whole. Content is one ranking factor, the page's title is another separate factor. Combined they help determine the relativity of page for a given search term.
Each page is judged on its own merits (domain wide penalties are not part of the ranking algorithm. They are part of the anti-spam algorithm. Matt Cutts heads that team at Google). This means there is no direct correlation between one page's rankings and another's. In other words, just because one page on the site ranks well for a phrase it doesn't mean another page on the same site will as well.
However, because links have value, one page can "boost" another page's rankings by linking to it. PageRank, anchor text, the relativity of the linking page, and more all can help the receiving page increase in rankings. How much it helps depends on the above factors as well as the competition for the search phrases being targeted.
When done properly, a well built website can create a hierarchy of content that emphasizes its main pages (categories). Typically such a design looks like a pyramid when laid out on paper. So, depending on the competition, the quality of content, and website structure, a website can achieve a relatively good ranking through internal SEO alone (more for less competitive phrases then actual competitive ones).