1) Check whether Microsoft SQL service is started?
Start->Programs->Microsoft SQL Server->Configuration Tools->SQL Server Configuration Manager.
From the configuration manager assure that the SQL Service is started.
2) Make sure you are entering correct Server Name.
Hope this will help you.
While installing the Sql Server, you need to choose the Default instance and keep it in Windows Authentication. Once you do that during the installation, a default instance of the Sql Server will be installed in your machine and then you can access it. There should not be any issue when using the Windows Authentication. Once it is successful, you can create the users and then you can make the sql server authentication to access it
Hope ti will be helpful to you.
Pawan Awasthi(DNS MVM)
+91 8123489140 (whatsApp), +60 14365 1476(Malaysia)
Your first error message clearly says that you have opened it using the design i.e., through user interface. Try to close it and once restart the sql server in the services by typing services.msc in run command.
Where as your second error of verify instance is due to incorrect server type and server name.
If you have installed in default instance mode then your server name will be MSSQLSERVER else the server name will be your PC name.
Go to properties of mycomputer and check the name of PC.
Give the PC name as server name.
For example my pc name is sri the the server name will be sri.
Then connect with windows authentication mode.
Editor: DNS Forum.