-No key in the ignition
-New (known good) battery installed
-Positive Cable connected
-When Negative placed on post .... starting motor runs continuously
-Plunger does not engage (fortunately) - so engine did not turn over.

Background:
-This car had been stored for ~three years, with battery removed.
-The car has been stored in a garage - dry and temp never below 35 F degrees.
-The car operated fine before the car was stored, especially the starter - no problems.
-No one touched/tampered with the car in storage.
-I have driven 99% of the miles (~96K) and it has been serviced properly.
-Cable connections @ battery and starting motor are clean, corrosion free and tight.

What happened?
(my ~guess~ is a relay is closed that should be open. But please ignore my guess, OK?

 

For starter to turn the solenoid on the starter must be shorted closed. It may be frozen from rust or dried oil. Remove starter and clean/check the solenoid and starter bendix movement, or replace the starter.

good luck