When I turn the key to "on," the radiator fan starts running and does not turn off without disconnecting the battery.   The check engine light, and the oil pressure warning light both come on.  The temperature gauge also moves into the bottom of the normal range.   When I turn the key to "start" nothing happens with the starter.  I removed the starter and had it tested.  It works.  I also tested the starter relay.  Powered, and unpowered it checks out.  The fusible links associated with the starter circuit both look good.  Any insight would be much appreciated.

 

Looks to me as though the coolant temperature sensor is disconnected, bad, or improperly grounded (or shorting). Check engine light would apply to that. Oil pressure light always goes on when you have the engine in Run but not running. Temp gauge is the giveaway. Fan runs because the car detects bad coolant temp sensor.

Code reader is your friend!!