2000 Pontiac Grand Am GT Ignition Problem

I have a 2000 Pontiac Grand Am GT1, with currently 115,000 miles on it. I realy have never had too much trouble with this car until recently. When I tunr the key to the run position everything lights up and I can hear the fuel pump run, but when I turn the key to the start position, nothing. It tends to do this more in the mornings after the car has sat overnight. If I sit there and turn the key over and over usually it will fire eventually. SOmetimes it takes 2 turns sometimes it takes 15 minutes of turning the key. I replaced the ignition switch with little to no improvment. Any help or advice on this probelm would be greatly appreciated.