Can you still FTP to your site directory? If so, then you can rename that directory to your new domain like this:
1) Create a new Fully Hosted Domain in Manage domains owned by the same user as your old domain. This will create a new example.com folder in that directory
2) Rename the new example.com directory to example.sav and rename your old example.com to the new domain name.
3) You'll need to create a new database host name in MySQL Databases that uses your new domain name.
4) Change your WordPress wp-config.php file to use the new database host name
5) Log into wp-admin and go to the General Settings to update your domain path.