[V8] Starter or switch?

[george.fallot at verizon.net]

HI,I recently noticed that the starter does not engage at times.
   It seems that I don't turn the key far enough.It has always 
started on the second or third time I turn the key. I replaced the  
starter last winter, so I am leaning towards the switch being bad 
not the solenoid. Besides getting under the car when it doesn't turn
 over is there another way to trouble shoot this?
I have 153k on this car, maybe the switch needs to be replaced?
    Thanks,George