You should start by checking the error log and/or the startup message log when managing the instance using MySQL Workbench. There could be clues as to what is going wrong, which may be different than this scenario.
When I had this issue, it was because I used a space in the service name during installation. While it is technically valid, you should not do that. It seems that the MySQL Installer (and MySQL Notifier) does not put the name in quotes which causes it to use an incorrect service name later on. There are two ways to fix the problem (all commands should be run from an elevated command prompt).
The first is to simply reinstall MySQL Server 5.6 using the default, no-space service name MySQL56.
The installer uses the same value for the service name and service display name. The name that I had originally specified was for a display name, when it should have been a simple service name. After installation, if you so choose, the display name can safely be changed to use spaces and other characters by using:
sc config MySQL56 DisplayName= "MySQL 5.6"
If you don't want to reinstall the server however, you will have to recreate the service. Start by removing the old service:
mysqld --remove "service_name"
Now install the replacement. You can use --install to create a service that starts with the system automatically, or --install-manual to create a service that requires you to start it.
mysqld --install-manual "service_name" --local-service --defaults-file="C:\path\to\mysql\my.ini"
This creates a service that runs as the LocalService account which presents anonymous credentials on the network however. Under most circumstances this is fine, but if you want to use the NetworkService account (which is what the installer creates the service as) you can change it using the Services administrative tool.