I realise that the position of the ad depends to a large degree on how long visitors stay on the site so here's a hypothetical question - what would happen if competitors made multiple clicks on a site using different IP addresses and stayed only for a fraction of a second each time? could this be used as a way to crush competition, I wonder? Alternatively what if an advertiser, again using different IP addresses (not difficult; I for example have got two ADSL lines and three dial-up accounts) could this boost a site into a higher position for the first vital initial week or so?
Six clicks is way too small a number from which to draw any conclusions. People landing on your page and exiting immediately usually means they could tell quickly they didn't find that they were looking for. That doesn't mean you didn't have interesting content, just not what they were interested in. Consider the following examples:
Someone looking for lyrics to a song sees that you just sell the CD or review it.
Someone looking for a repair manual just sees a storefront for the item.
Someone looking for the premium version of the product sees your page for the basic version.
There are a plenty more. Study your logs and see if you can determine what search keywords were used to generate your clicks, then use negative keywords to filter out unwanted ones.
In working with my own account and being hired to work on several others, I've found newly open accounts seem to have a harder time establishing a good quality score. This leads to higher minimum bids and lower positions. This may or may not be objectively true, but it's been my experience.
That having been said, I'm not sure if a keyword with 8+ pages of advertisers is the best place to start. I'd begin with less competitive terms, maybe some misspellings and/or long tails. Once you develop some performance history, you can bring your battle to the big boys on a more level playing field.
Good luck.
