tearing my hair out to be honest at this stage.
I have an installation of SQL Server 2008 express on my laptop. I\'ve been trying to login to SQL Server Management
Try to give only your machine name.
Like if it is Your machine name/serverInstance
so simply give it only your machine name
then try to login.
Explanation why this trick works: here Microsoft writes
An instance is either the default instance or a named instance. The default instance name is MSSQLSERVER. It does not require a client to specify the name of the instance to make a connection.
So if you created default instance (MSSQLSERVER) or named instance with name MSSQLSERVER you then should not add the instance name but just use the server's name (your machine name).