1999 Monte Carlo

I have a 1999 Monte Carlo with a 3.8 litre motor. It has 150,000 miles on it. My problem is when I turn on the key I have all power including headlights and the fuel pump is running. But when I try to start it nothing happens. The starter will not even start to engage. I have replaced the starter, safety neutral switch, and a new key. I have also even replaced the battery. The security light still stays flashing. I have checked all fuses and relays and they checked good. The motor will start and run if you jumper off of the selonoid on starter. Your help would greatly be appreciated in this matter.