Delete WP Blog

I am unable to get into my blog any longer due to a bad plug in and GoDaddys answer was to close the site down because I was unable to remove the plug in and my security question name and answers appeared when you clicked on my site. My question is can I delete my original site so I can start another with the same name I no longer have hosting and am looking at a new host but I want to get everything in order before I lay down more coin.