I got this information from GoDaddy. It fixed the problem.
I understand that you are experiencing issues with uploads through WordPress. The most common issues that cause this on Virtual Dedicated Servers is Permissions and PHP Mode. With wordpress you need to ensure that your Uploads folder, typically under the wp-content folder, is set with write permissions. You can do this through the Plesk File Manager by clicking on the letters to the right of the folder name that look like "rwxr_xr_x". If they had write permissions they would like like "rwxrwxrwx".
The other common issue is the PHP mode. PHP will be set as an Apache module by default. This will cause any files uploaded by PHP, and wordpress as a PHP application, to be generated with the user and group root. As you are using plesk files created with the user and group root cannot be modified, moved, or deleted by your plesk user. To work around this you can set PHP to run as a FastCGI module. This will then make any files generated by PHP and your WordPress application be created as your Plesk user so you can interact with them freely. You can change this by logging into Plesk, selecting domains, selecting control panel to the right of your domain, selecting Websites & Domains, scroll to the bottom of your screen and click on the domain name. In this screen you will see a line that states "PHP Support (run as" with the module type in a drop down menu next to it. You can change it to FastCGI here and then select okay at the bottom.