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If Google did consider the class or id names as part of the text then people would be making sure they were full of keywords for their sites and it would be listed on SEOMoz as a spammy tactic. As that's not the case I would say that Google doesn't include it. Also you shouldn't be worrying too much about Keyword density - http://www.seomoz.org/blog/10-myths-that-scare-seos-but-shouldnt-whiteboard-friday

Hi! The most common reasons for this are discussed at https://seomoz.zendesk.com/entries/409821-why-isn-t-my-site-being-crawled-you-re-not-crawling-all-my-pages. If that doesn't solve your problem, please visit our help hub at http://www.seomoz.org/help and contact our help team to open a ticket.