Can I restore the defult SQL Server Public Role?
Well, this would be the script to restore the connection permissions to the defaults.

use [master]
GO
GRANT CONNECT ON ENDPOINT::[TSQL Default TCP] TO [public] AS [sa]
GRANT CONNECT ON ENDPOINT::[TSQL Default VIA] TO [public] AS [sa]
GRANT CONNECT ON ENDPOINT::[TSQL Local Machine] TO [public] AS [sa]
GRANT CONNECT ON ENDPOINT::[TSQL Named Pipes] TO [public] AS [sa]


If that doesn't work, try stopping SQL Server, starting it in single user mode ("sqlservr.exe -m" from an administrator command prompt), connecting with sqlcmd.exe (which will default to the local default instance with Windows authentication), and running the script that way.