A WebmasterWorld member is reporting that she has purchased a domain from a third-party domain provider and has built a website upon the domain that seems to be pretty Kosher. Her site, however, is not being indexed.
What she does know is that the Internet Wayback Machine indicates that the domain was spammy prior to her ownership of the domain. She, therefore, needs to submit a reinclusion request.
How do you do a reinclusion request? Go to Google Webmaster Central and click on Webmaster Tools. You will then see a list of sites you maintain and there is an option to "Submit a reconsideration request." This will only work if your site is verified.
On the next screen, you are instructed to only utilize the reconsideration request if your site had previously violated the guidelines (but was subsequently cleaned up) or if you recently acquired a domain which may have previously violated these guidelines. This appears to be the case for the WebmasterWorld member.
You can then select your verified site from the drop down and fill out information regarding why Google should reconsider it and you should be seeing a change within the next few weeks.
Google specifically has an option for submitting "reconsideration requests" for sites that you "recently acquired which you suspect may have previously violated" Google's webmaster guidelines.
Forum discussion at WebmasterWorld.