Pinging your website will NOT get it unbanned. You need to sign up to Google Webmaster tools and look at your links. Create a Google Docs spreadsheet of all the bad links and start contacting the webmasters to have the bad links removed. These include links in bad neighbour hoods and links with too much duplicate anchor text. Once you have made reasonable effort to remove bad links you need to submit your site through webmaster tools for re-evaluation. Provide access to Google docs spread sheet and the contacts you have made. Getting your site indexed again is a manual process, so as long as you can show Google you have done the right thing they may help. The Google Docs spread sheet with list of contacts, responses etc will help. If a webmaster asks for payment to remove link, note on spread sheet and move on to next one. Google will advise what else needs to be done if they are not happy with your efforts. It is a long process but can be done. The alternative is to dump your domain and start again.
Give up domain name unless it is extra ordinarily good and you haven't put much effort to create that website. If the domain is good and you have put good efforts to create that website, submit a request to Google for site reconsideration. Before you contact Google, make sure you have taken necessary action to make your website comply with Google guidelines. If you aren't much of tech savvy, hire someone who can help you with this. Once the site is re-structured (if the reason for site ban was bad links, make sure you removed all bad links, or it is banned by bad architecture or something) as per Google guidelines, put a request for reconsideration.
Pinging is not useful for banned sites or any normal sites as well. Let your content index naturally. If you tracked over-pinging then won't be good for your site.