Delta requires your SkyMiles PIN to complete any transaction on the phone. If you have forgotten your PIN, or have never created one, they can't reset or retrieve it, but can offer to email it to the email address you have on file. If you don't have an email address on file, or the email address is outdated...you're done. The only option is to mail or fax a request into their customer service department.
Delta.com wants me to pick two new security questions. (Annoying) I fill them out and it won't take them - it resets the page asking for me to fill it out again.