Try restore from backup. Create a new backup and then restore it to new location / or as a new name, to build a new database. I find this has the least problems. If it is to different server copy the backup file to the server first, then restore from it.
The copy database wizard often has errors especially with larger more complex databases.
In this case I would assume that the server name was entered incorrectly or there is a firewall issue between the server and the machine you are running the wizard on.