SSMS should not have anything to do with the firewall though.
Did you try this?
Go to Control Panel -> Programs -> Program and Features -> Select your current version of Microsoft SQL Server
Right Click, select Change/Uninstall
Click Add features
Select the backup copy folder
Do the steps what you done for SQL Server installation until features selection
Now select the features Management Tools Basic/Complete or both
And go ahead with process for complete installation.
Now you should get, SQL Server Management Studio and you can browse your databases.