There were already two instances of SQL Server 2012 and 2014 (each), and SQL Server 2012 was installed. This installation overwrote a number of .dll’s in the SQL Server browser, which caused the service to crash.
A repair installation using the SQL Server 2014 medium reliably fixed these problems.
The use of several SQL Server versions in an operating system environment is not advisable, especially for productive systems. On no account should more recent and then older versions of SQL Server be installed in an operating system environment. If one or several instances are already running in a relevant operating system environment, installation should take place within the maintenance window for these instances and of course only after production of database backups.
Database consistency checks are absolutely essential to keep SQL Server up and running smoothly. Conduct them with every full backup, monitor the result of job completion and the status of SQL Server services, and use the checksums for page verification in your databases.