Let me give you some simple things to do, and if they don't work, then do what gearheadnick wrote.
Assuming all your components are good (battery, connections, and starter), here's a quick 1-2-3:
(1) Just to be clear, was the starter solenoid replaced as well (it is usually replaced with the starter, but I am double checking). If not, then I would suspect that to be your problem.
(2) Will it start when you place the shifter into NEUTRAL? If so, then your neutral safety switch is defective.
(3) The horn relay and the Engine Starter Motor Relay in the Power Distribution Center are likely the same. Switch them and see if it will start. If it does, your relay is bad.