The number one thing to check would be that everything with the connection is the same. Typically, in a server move there may be slight differences or maybe a user account in the database changed during this process or is there but no longer valid. It is your hosting provider or server administrator’s responsibility to provide you with valid connection details to connect to your database if you do not have managed support with your hosting provider, it may time to invest in it if you are not comfortable with this process (or take a look at our Cloud platform and never have to worry about this again 🙂 ). Check all details from the host name, port, socket, database name, database user and password are critical when changing servers/hosting providers.
If all the host, port, socket, and database name are correct. I’d try creating a new database user, giving them full access to the database and re-inserting the database username and password in the conf_global.php so you know 100% everything is correct.