Just a quick note in case this causes someone some trouble.

The ApplicationsInsights.config file is ignored by default when a project is added to source control; or at least was in a recent instance. Created a clean project using the ASP.NET web app template with Application Insights enabled.  When this was added to Git, the ApplicationInsights.config was ignored resulting in the following build error:

error MSB3030: Could not copy the file "C:\a\1\s\MSDNAzureDevBlog\ApplicationInsights.config" because it was not found.

The simple solution is to not ignore the file in order to get the build to work.

Should note that a better solution would be either Alex's suggestion of a pre-build step to supply the config file or using Slow Cheetah to transform the content of the configuration file (re., supplying the correct instrumentation key).