99n Dodge Ram 1500 P/U clicks, then starts, intermittent
 

When I turn the key, it just clicks, sounds like the solenoid engages, but the starter doesn't turn. Sounds like the battery connection, but I have new terminals and the battery is good. When it does turn over, it turns strong and starts right up. I'll turn the key several times and I get the "click", then it starts.
I was thinking it might be the neutral safety switch; it seems that I can move the gear shift lever on the column just a little and it starts, but I'm just not sure that moving the lever makes it start.
Any ideas or suggestions?

Check tranny linkage. It should not do anything except in Park and Neutral. It may be off slightly. Also check the ground cable where it bolts to block by power steering pump and make sure the connection is clean and tight. Corrosion there will keep from making good contact.

If I move the lever to park or drive, it doesn't even click.
It only clicks and starts in P or N.
Could it be the ignition switch?

Here's a short video...
http://static.photobucket.com/player.../VIDEO0084.mp4

After reading some posts, I'm thinking it might be the starter.

If you get the solid click from the starter, but, the starter doesn't wanna roll the engine over, starter motor is most likely the problem.