Hello Shruti;
There could be any number of factors to contribute to this. I recommend calling standard support at 866-518-5689 so that support can look closely into your account, and provide optimization recommendations.
2000+ impressions and no clicks is definately an issue, and i can't see position would be a factor. Higher poition does provide a higher click through rate, but you should still see SOME action.
I would not recommend making many ad groups and spread your keywords around. I understand what the previous poster is saying, but dynamic text insertion will accomplish this, and provide more relevancy.
Also, at this point, historical data plays a role. Try copying everything over to a new campaign/ad group and delete the poor performing one. With 2000 impressions and 0 clicks, it's deemed a poor performing ad. Wipe the historical data and try again.