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How does really old school HTML (with inline CSS and a boat load of markup errors) affect modern SEO? I'm talking purely rankings, not conversions or bounce rate etc.

One of my clients has a site in a niche market, and has been ranking well for years. Since the Penguin algorithm changes his site dropped and 4-5 other sites came out of nowhere to take to top spots. These are very large sites, but they are not really reliant to the search terms. Sure, they sell one or two of the niche products, but our site is dedicated to those products. The site has been updated since I took over on the site, and is well SEOed. The site in question still ranks 1st for the keywords in every other search engine imaginable. Has anyone else encountered this? If so, how did you combat it?