getttng a domain unbanned from google.

call them and beg ;)

start by asking them why/if it was/is banned

Your best bet is to email google and submit a reinclusion request. Explain that your domain was banned when you bought it. Sometimes it takes a long while (6 months or more) and sometimes they do it quickly. Make sure your domain has nothing spammy on it either, they may actually human-review it before reincluding it in the search results. I had one domain that was banned when I bought it and it took a long while, but they did finally put it back in the index and even has some PR now. If you email them a few times, and your site genuinely is surfer-friendly and has some content, then they will reindex it.