Can I sue Google?

Google Adwords has a policy of not allowing advertisers to have more than 1 advert per company per keyword if the website/s that they link to offer the same services or products. In other words a single company cannot buy more than 1 advert for the same keyword. Google's policy can be found here: Can I show more than one of my ads on a page? - AdWords Help

I have reported a company to Google that has numerous adverts running for the same keyword. Google has 'investigated' and decided that there is no link between these adverts/clients and the company that I know is running them. I have explained to Google that this 1 particular company is running all of these adverts and that this company is manipulating the cost of other advertisers (in essence fraud) bidding on the same keywords. Google has rejected my offers to prove the connection between this single company and these adverts and has told me that they will decide if there is a connection or not. Basically Google is allowing this advertiser to continue because they are earning Google a lot of money.

So can I sue Google for having a policy that they are not enforcing in order to make more money and at the same time disadvantaging advertisers who are following their rules and allowing rogue advertisers to push up the advertising costs of legitimate advertisers?

You certainly can try. The firm obviously has a great deal of resources so unless a lawyer will take it on contingency it could be expensive.