Starting problem

I just just bought a 97' GTP with around 140k on it. Auto trans. I had thought I had a starter problem. I would go out to my car to start it and get a small click when I turned the key. Some times it would start but sometimes it wont. Check voltage at battery. Always over 12 volts. cleaned and checked battery conections. All wires look clean and no corosion at the starter. Was thinking bad starter. So I replaced the starter. 2 days later same problem. Any help on what else could be wrong? I am not sure if it is related but my key will stick in the ingnition lock. Will replacing it help this problem? How do I get the old key lock out. I know there is a trick but dont know it.
Thank You for any help.

First, have the battery checked. It's possible to have 12 volts but not enough amperage to turn the car over. If the battery passes a load test, then you may be experiencing the first symptoms of a bad ignition switch/harness, fairly common in GP's.