SQL Server 2008 R2 Ent trial expired move to express?
So someone let our SQL server 2008 R2 enterprise trial expire on a production web server


Violation of the EULA.


  Is express or compact capable of running a small website?


Both are capable of running a small website. Express is also capable of running medium or large websites. Personally I would go for Express if possible, Express handles concurrent access much better than Compact.


  Is it possible downgrade to express or compact and how?


Uninstall Enterprise, install Express and migrate the database to the new instance. Compact is much harder - Microsoft has no tools for downgrading to Compact. This tool, amongst others, can help you.


  How can I backup the existing databases now that we have been effectively locked out of them?


You might try starting the database in single user mode, or stopping the SQL Server service and getting the MDF and LDF files out of the DATA directory and attaching them to the Express instance.