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I had the same problem even with dedicated server. I had to upgrade CPU a week ago to solve my problem. My problem is to much queries and big tables.
You can find this useful, I did, it saved my life a couple of times:
http://www.xuups.com/modules/publisher/article.php?storyid=12This hack will enable you to see what queries are taking to long. By knowing that you may take providences like, changing the query or set up indexes.
The problem may also be in some module function.
Please check timers on your debug and see if you have a module taking to much time to load.
In my case the cpu load has not much to do with the number of page requests, it is more related with the size of the tables. For each item added the more slow it gets.