The first line of that whole error is all that you need to worry about:
Access denied for user 'wwwp1designcoma'@'localhost' (using password: NO)
Fix that, and the rest should fall into place.
What the error is telling you is that the database user that you've set up has the wrong password saved, so I'd advise you to go and double-check what you've got in your wp-config.php file and make sure that the database connection details in there are correct. Just remember that on a new server, there can be different settings needed, so if you are having a problem with it the first place to ask is your hosting comapny as they'll be able to tell you exactly what you need to use for those settings.