Wow, your replaced the starter? No small task. Did you use a proven starter? Remember most of the parts houses can do a bench test on a starter.
I agree that there is likely a electrical issue. There are all sorts of relays, sensors, and switches that can go belly up and prevent starting. After a couple of embarrassing non-starts ... I installed a permanent jumper wire from the 12v control terminal on the starter up to the battery area ... neatly, and securely stowed near the battery. When I get a no-start, I place the tranny in P, raise the hood and touch my jumper wire's bare end to the positive terminal of battery. Never fails! It jumps around all that "stuff" that can fail.