Now its me.  As I turn the key the oil light comes up for a half second then it goes out, then I turn to start and NOTHING.  When I go the car first time, it was starting with difficulty and later just did not.  

Would it be the switch?  What is that thing with the oil light and that the battery light does not come on at all, not even for that half second.  

I just cleaned all the ground connections that goes to the starter, the battery is strong.  I tested the starter out of the engine with the jumper cable and the solenoid clicked and the motor ran.  I had it in a bell housing to have the bushing for it.  

So, I guess this is not a common thing and hopefully some of you could answer it.
With respect to the Honorable Members of the List,
Zoltan