You just bought a new domain for your site, but what else did you buy? Just like with a used car and checking out the Carfax report, you may want to do some checking.
It does happen that a newly-launched site doesn’t rank or ranks poorly even after giving it some time. In a case like this, it could be that the domain you just bought was used before and has a less-than-stellar history. On Twitter, Google folks have suggested that these things can happen if the domain had been used previously by a site with a “spammy past.”
So, what to do? Check that domain out first. Look into its history (use archive tools like wayback machine or Google analytics if you can) to check it out. If it appears that your new domain has a dark history, ask Google to reconsider. Use your Google Webmasters account to submit resubmit your site for reconsideration and see what happens.