RichH - 10:49 am on Jan 1, 2013 (gmt 0)
My guesses would be that your site is either simply not appearing high enough in the SERPS for anyone to find it, or that the page title and/or snippet of info that appears below your site's entry in the SERPS isn't compelling people to click on it. Is it in a highly competitive niche? Are you getting any impressions in the SERPS at all?
In contrast to your experience, being rather bored over Christmas I published a new mini site. Just 2 pages, 2000 words, a couple of dozen pictures, exact match domain name in a rather specialised travel niche. I did some basic on-page SEO but didn't cover everything I might have done. The site has no back links at all. To speed up indexing I filled out Bing's online site submission form and added it to my Google Webmaster Tools account.
The site was indexed by Google within 24 hours and within 72 hours was appearing in the top 5 for my chosen search keyword phrase. Bing indexed the site in 72 hours and it went straight in at number 2 in the SERPS for the same keyword phrase. The site is already getting some traffic. Not a lot, as its niche is quite esoteric so I wouldn't expect many people to be searching for this kind of thing, especially at this time of year, but it's certainly getting impressions in the SERPS and people are clicking.
As to SEO analysis, apart from sifting through the advice provided on this very forum, I'd start by looking at the SEO analysis tool in Bing's Webmaster Tools which should highlight any major problems.