[QUOTE=bentcipher;144914]
Note that if you put the shifter in gear and try to start then you actually don't even get a click - it makes no sounds. So the symptoms are different from what I'm having.QUOTE]

It clicks in Park and Neutral is correct. It should not click when it's in a gear so thats ok and normal.

I'm still thinking it's a loose ground or bad connection. Try this "old school" trick. Have yourself or someone tap the starter while someone turns the key. But don't tap until the person running the key has tried, turn the key and if there's nothing tell them to tap the starter while the key is still being turned. I know it's old school but worth a try...Good Luck