This has happened to my maybe 3 times over the past year. Turn key...nothin'. No crank click clank or clunk whatsoever. Happens more often when it'* cold outside (brand new batery, btw). When I get pissed and go open the hood the car the car starts right up!

What could it be? starter solenoid, ignition key sensor, transmission sensor ( when in park), ignition switch?

Thanks!

When you put your key in the ignition, does your security light go off. Its possible that you have something wrong with the Pass Key II system? If the security light doesn't go off, and starts flashing the system has detected a faulty. Most of the time its a problem with the lock cylinder. I've by-passed the system before in several GM cars that I owned using a resistor of the same valve as the resistor pellet in your key. Its possible that you have a bad starter.

First thing i would try, even though its a new battery, unhook the terminals, clean them, then put them back in, make sure they are really nice and snug, you would be suprised at how many times this has caused others problems

Wipe off the little black chip on your key and see if this helps. If it gets dirty, the Security won't let you start the car. Happened with mine.

Do the lights on your dash all come on when you turn the key but nothing happens with the starter when you turn the key further?

Do you have another key? Try using it and see what happens. REmember when you turn the key 3 times if it'* not getting the right reading from the resistor chip, the computer locks out starting for 3 or 5 minutes. Then it will try to read the key again.

If it'* a dirty key contact, try rubbing with a pencil eraser.

good points, could be the pass key system or bad grounds to the Batt or engine.
I would try the alternate key thing first, cleaning all the contacts.
Also clean all the under hood grounds in additin to the Batt connections.