you will need to update the Connections/PowerCMSConnection.php file to use the correct details for connecting to the new MySQL Server.
also, when you add a content area to the page, the path to the WA_CMS/addtosite.php page is generated based on that servers file system,
if you open the PCMS Admin section and select a content area, then view the Developer notes ., it will show the include path for the WA_CMS/addtosite.php file for the server you are on.
you will need to update the code on your pages to use that new path.