Was the "NEW" button previously available and then disappeared? Did you just sign up for a new DocuSign account?
Based on the above I can think of two possibilities....
1) The most common is that the Permission Set assigned to the DocuSign User does not have the permission called "Can send envelope". If this permission is not enabled then the DocuSign User would not have the ability to create an envelope.
2) Under the circumstance where you created a new account, I have heard the interface or UI is different and it no longer uses the "New" button rather something else.