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Can you give a bit more details?
Is the domain still the same?
If it is, you just should need to update your wp-config.php - access it by ftp and open it with a text editor, then edit username and database name and maybe password inside.
Same for the config.inc.php of Coppermine (in the includes folder I think, I myself never used coppermine)
Did you move through cPanel? Then the passwords might still be the same, but if not, you can set them through cPanel -> databases -> mysql databases -> scroll down to Current Users. There are also the detailed names of your database and mysql users listed.
If you used affiliationally, you need to edit the path of your include codes.