Chrysler - Towncountry :: 2008 - Won't Start Sporadically

My 2008 Chrysler Town & Country has, since it was 2 mos. old, had a "no-start" problem. This is not a stalling problem. It happens when the car is off and I try to turn it on. The problem is very sporadic (sometimes several times a day - I do lots of short drives - sometimes several times over the course of a few weeks, then no problems for months). When I turn the key in the ignition, all electrical components come on (dashboard lights, air, radio, etc.) but nothing happens with the engine (it does not make a sound). The dealer has replaced a computer component, the battery, the starter, the electronic keys but the problem always happens again (within a few days of it the "repair"). I usually have to turn the key 3-12 times (sometimes I take it out of the ignition, sometimes I pray!) and eventually the engine starts. Because the problem is sporadic, the dealer has not been able to replicate the problem (though they have, at times, had it for a week or more and even driven it as if it were their own, home at night, to work, to run errands). Although the car eventually starts, it is very problematic when I have to be somewhere and it takes 10 minutes (not to mention a lot of worrying) to get it started.