Check the sql log in the LOG directory of your instance – see if anything is going on there. You’ll need to stop the service to open the log – or restart and you can read the old one – named with .1 on the end.
With the error you’re getting, you need to enable TCP/IP or Named pipes for named connections. Shared memory connection should work, but you seem to not be using that. Are you trying to connect through SSMS?
In my log I see entries like this…
Server local connection provider is ready to accept connection on [\\.\pipe\mssql$sqlexpress\sql\query ]
As the comments said, .\SQLEXPRESS should work. Also worstationName\SQLEXPRESS will work.