If you installed Express edition, your sid or service should be XE, so this error implies the database isn't up.
Open a command window and type
This should show what services are running (if any).
This will show the connection definition being used. It is what you would expect? Are host, port and sid or service correct?
Do they match what you have entered for your connection definition in SQL Developer?
If the definitions seem OK, try using the start menu options to stop and start the XE database and try connectiing again.