I had starting issues on my truck couple of years ago. Ex-wife went to store, and when she was leaving a parking lot, truck wouldn't start. She got ride home and left the truck, when I got off from work I went to see what's the problem. First I crawled under the truck to see if NSS-connector is good, because it had been problematic. That was ok, so I went to start. Nothing, just a loud click but the engine didn't turn over. So I figured the solenoid is bad, and tried to connecting the starter terminals, and got the engine running. Kept driving it like that for couple of days, until I had time to fix the starter. Then one day my co-worker happend to be on a parking lot when I was leaving, and I asked him to turn the key, while I listened the starter. That loud click, it wasn't the starter solenoid, it was a shutdown solenoid (diesel) which pops open when the engine is started. Normally that happens at the same time when the starter is engaged, so you really can't hear it if you don't know. Nowadays I do hear it just before starter.
Anyways, shut-off solenoid clicking leaded to think that there is something on wire between the PDC and the starter. So I went home, and later that evening started to look for a corroded wire, so I followed the wire from a starter, and found a connector below the battery. Loose connector, to be exact. Seemed to be ok, no corrosion, so plugged it in and started the engine! I had the whole front end apart over a year before that incident, and when I put everyhing back together, I didn't check that I had pushed the connector all the way in.

 

You're not going to hurt anything with a push button starter unless you use a switch that can't handle the current. Most of the time, using an under rated switch will just burn out the switch but they can also internally short and basically weld themselves shut meaning that they won't open again when you release the button. Its a lot of current. Just last week I purchased a remote starter switch from Autozone for under $20. It has two clips to attach to the starter and is designed to deal with the current flow.

The wiring and voltage path for the starter circuit is fairly straight forward and even the consumer level repair manuals provide a decent diagram. Stop guessing and follow troubleshoot the circuit using a diagram and you'll find the problem. A cup of coffee, a warm room, and the wiring diagram will show you where to look.