This is the exact problem we're having on the exact truck. http://forums.automotive.com/70/8265751/engine/2003-silverado-wont-start/index.html The truck will not start, but doesn't have any power issues (battery fine, indicators and lights etc.) But it won't start, not click or nothing. I've unplugged the battery, the connections to the transmission (shifter...no idea what it's called), and still nada. Truck says it's in second gear when you turn the ignition. 2003 Silverado HD. It's in park though, and I've tried moving it through all the gears (neutral, park,OD, 2,1...etc.) The link shows the guy having the exact same issue, but he pulls an Almu and never gets back to the group with what happened (if it was the starter or mechanisms etc.) Any advise? I just signed up to PM that guy, but doubt I'll hear anything.
Considering the car indicated it's in second gear when trying to start I'd say you got a bad neutral safety switch which you can try cleaning the connections and try it or just replace it. The part is cheap and shouldn't take long.
