I have work out a experiment: I make two website on the same day. add content to it ,and submit the website to goolge ,also the sitemap!!! but I use google adwords to buy traffice to one website. One month passed! The website which I buy traffic from google adword has only one page indexed in google. The website which I don't buy traffic from google get all its page indexed on goolge. So I guess adword will have some affection on the pages indexed on Google.
Interesting. Perhaps Google counts the quality of traffic coming to a site. It certainly does with its adsense program.
You can't draw conclusions from a sample of two examples. I see lots of sites that do well in natural search and also do PPC.
Are both sites identical?... likely not and therefore one may be in a more competitive area than the other and in the 'sandbox' It should rectify itself in the future - but it is like comparing apples and oranges really. You should still continue to carry out SEO and build links to both sites as you normally would and in time both sites will be fully indexed.