The 'DefaultConnection-Web.config Connection String' argument cannot be null or empty. VS2013

Fixed by removing the following markup from the .pubxml file. You must exit/restart VS after removing the markup (or VS will add it back in).

<ItemGroup>
  <MSDeployParameterValue Include="$(DeployParameterPrefix)DefaultConnection-Web.config Connection String" />
</ItemGroup>

Reason of the problem is one of the followings:

1. Change the name of the connection string in the web.config.
2. Add a new connection string in the web.config

Solution

1. Select the website project, right-click on it, and click publish.

2. Press the settings link and from the pop-up window select the 'Settings' Tab

3. Uncheck the use this connection string at runtime from all your connection strings.

4. Click the Save button to close the window. (No need to restart Visual Studio)
5. Try to publish the website again, and it should publish without a problem.
6. You can reconfigure the settings as it was previously, the unchecking just triggers VS to regenerate the .pubxml file, So you are not forced to change your settings at all.

NOTE
I am using VS 2017 (and according to the comments this also work in Visual Studio 2013)

Just for Note
After I did the previous steps, I noticed that the .pubxml file changed automatically. here is the difference which has been made (automatically without any interference from me)

So I think this is a better way because it is easier for the developer and also it let the visual studio to solve its problems himself, without forcing it into a specific thing.

Create a Parameters.xml file in the Project root with the following content:

<?xml version="1.0" encoding="utf-8" ?>
<parameters>
  <parameter name="DefaultConnection-Web.config Connection String"
      description="DefaultConnection"
      defaultValue="Server=tcp:x.database.windows.net,1433;Database=x_db;User ID=x@y;Password=z;Trusted_Connection=False;etc." tags="" />
</parameters>

All the other missing config elements can be added here as well.