You need to use the Addon Domains mamager at your cpanel and and add it that way. You don't need to add the WWW to the name because it automatically gets added. You also need to use NS Records.
FTP this small text file to your site and give it a .pl extension and chmod to 755 and see if it works for you.
http://byrondallas.heliohost.org/time.txt
Yeah the cpanel just thinks that it's a dedicated ip. What you need to do is start a new topic (Request For Dedicated IP) in this forum (Customer Service) and post your username and domain name and either me or Wizard will escalate it to djbob.
If you had an old account with that same name it was probably deleted because you failed to login to your cpanel every 30 days. Re-ceating a new account won't recover lost files. I'm sorry if you lost any old data but there's nothing we can do about that. You should always keep a backup of important data on your machine or on another server. Your new site however should be up within a day or two.
I can delete your account and let you re-register. Is that what you want to do?
Isn't this your account also?
http://denismedeiros.heliohost.org
It's showing as inactive, so you can either use it or I'll delete it also.