You probably do not have create database permissions. Did you specify windows authentication or SQL?
Personally I prefer to create the Db manually as I can create a separate sql login for nopcommerce.
Manual creation of database (presumes you have direct access to the SQL Server)
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1 - Open up SQL Server Management Studio and connect to your SQL Server. Your credentials must have create database privaledges)
2 - Right click Databases and choose "New Database"
3 - Give your database a recognisable name e.g. nopCommerceDB
4 - If you want to change the paths to your database files (default is "C:\Program Files\Microsoft SQL Server\MSSQL.1\MSSQL\DATA") then you can change the Path in the "Database Files" section.
5 - Click OK to create the database
With the database created, now we need access for our application so lets create a new SQL Server login and map this to the nopCommerceDB.
1 - With SQL Server Management Studio open, right click security (under the server node) and select "New > Login"
2 - Give your login a name e.g. "nopCommerceUser"
3 - Select SQL Server authentication (it is unlikely you will use Windows authentication in a public environment)
4 - Give your login a strong password - something like Hell0k1tty!
5 - Untick "Enforce password policy"
6 - At the bottom of new login window, select the nopCOmmerceDB from the Default Database drop down list.
7 - Next with the new login window still open, select "User Mapping" on the left hand side of the window.
8 - You will see a list of databases on your server. Tick the "Map" checkbox next to your nopCommerceDB database and in Default Schema, type "dbo"
9 - At the bottom of this window (Database Role Membership), tick "db_owner"
10 - Click OK to create the login.
Now if you expand the security > users node of your nopCommerceDB you will notice that SQL Server has automatically created the "nopCommerceUser" for that database.
So now we have access to the database. Next we need to add our nopCommerce database objects.
In the install directory of the nopCommerce their is a scripts directory that contain the database creation scripts.
Copy these to a location that you can access from sql server management studio.
1 - Open nopCommerce_createDatabase.sql in Management Studio
2 - Make sure that the context is set to your nopCommerceDB database (top left, select NopCommerceDB from dropdown)
3 - Click the "Execute" button or press F5 to run the script.
4 - You should get a message saying "Command(s) completed successfully."
5 - Now open nopCommerce_createData.sql
6 - Again, making sure you have your nopCOmmerceDB database selected, execute the script.
7 - This time you will get quite a few messages displaying how many rows were affected for different actions.
8 - All being well, expand your database in object explorer (on the left) and you should see some tables under tables.
So at this point we have created a database and have the necessary security in place to connect to it.
Now to edit web.config to connect to our database.
1 - Open up web.config and add the following within the <connectionStrings> nodes. You should end up with something like below:
<connectionStrings>
<add name="NopSqlConnection" connectionString="Data Source=YourServerName;Initial Catalog=YourDatabaseName;User ID=TheLoginNameYouCreated;Password=TheStrongPasswordYouGaveYourLoginName;"/>
</connectionStrings>
I have highlighted the things you will need to change depending on your configuration.
If you are in a hosted environment you may need to check with your host what the correct settings are.
Also in a hosted environment it's unlikely you will create the database or login through SSMS. Normally, you have an option to create a SQL Server database in your hosts control panel, as well as creating user accounts for that database (the user you create is then used in the connection string to connect to your db).
Hopefully that gives you the information you need to create the database manually.
I ran through the process myself as I wrote that so can confirm if you follow these steps it should work.
If you still get problems after this, try starting from scratch in IIS. Create a new Virtual Directory, make sure it's set as an application then copy the contents of nopCommerceWeb to the root directory. Make the changes to web config and then try navigating to the site.
Cheers,
Ben