Execute a derived constructor before the base constructor in C#

What you are trying to do is impossible in C#. A constructor in a base class must be run before the constructor of any derived class otherwise there would be potential for corrupt object state. A child object must be able to assume that its base is fully constructed and available.

IMHO your design is wrong. You shouldn't start the process from within the constructor. Your consuming code should explicitly call the Start() method when required.