97 Grand Prix won't start

I have a 1997 Grand Prix Gt. The problem that I am having is that when I go to start it, it won't turn over. If i turn the key 3 or 4 times it cranks right up. Sometimes I have to turn the key 150 -200 times before it will start. Most of the time it cranks just fine, but occasionally it does this, and I get stranded. My battery is good, and i can hear the relays both inside the car and in the engine compartment clicking. It is just like there is no current getting to the starter. All other elec. components work fine. Is there a lock out system that is not allowing the engine to turn over. I have used both sets of keys to no avail.

Do you have a small pellet on the key? If not I would suspect its in the Ing switch (cylinder) if your electrical inclined~ Pull the dash apart underneith the steering wheel, find the yellow(some are purple) wire and use a test light to see if when you turn the key that its powering up, if not I would suspect its in the column or cylinder. If there is power there, I would check it at the starter, maybe you have a seloniod thats acting up on the starter.... or a bad connection/wire to it.