E350 Starting Switch problems!!!

1994 7.3 Diesel:
 
Will turn over & start many times; other times, no fire to switch wire @ starting solenoid.
 
Replaced the solenoid (located on firewall in front of battery on driver's side): but tested voltage when it would not start (turn over) @ switch wire & zero voltage.
 
Will start everytime that I bypass switch & touch both main bolts together with screwdriver.
 
Any ideas?

Auto trans?
 
Same problem if you attempt a start it in neutral?

Have not tried it in neutral?  But since you mentioned this; the linkage needs adjusting cause when I put it in park, it will roll off at times. 

You hit the nail on the head; I put it in neutral, starts everytime, so I need to adjust the linkage.  Thanks for the input.