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If a site or web pages of the site is properly compiled with w3c compiler.
Does it helps in the ranking of the site in major search engines like google and Yahoo.
In other words does it shows any positive results in the ranking of the site......
No, to be quite brief and short in the answer.
Having webpages which are not W3C compliant can indeed hurt more or less your ranking, depending of type of errors found in your pages.
Considering that search engines may stop crawling your pages or missed links because of bad HTML, then it hurts your ranking/position.
Always have W3C compliant webpage, safer.
Also, get CSE HTML Validator, free HTML validator which helps to get on your mqchine the obvious HTML errors but less strict than W3C.