Car starts in ACC position?

Okay, that might make it easier as it sounds like the issue is voltage feeding back through the switch. Take a test light and see if there is voltage on the green wire at terminal 1 when the key is in the on position. Disable the injectors as I had you do above (remove SNSR fuse 3) Use a pin or needle to probe into the back of the connector with it connected to test that. The green with in pin 1 should only have power with the key in start. If it has power when the key moves into the run position, then there is a problem in the wiring that feeds the switch. To verify it isn't the switch use a multimeter to check between the same two terminals with the switch unplugged. While rare it could be that the switches are made poorly and causing the problem, although I think it's more likely in the wiring harness itself.

Yes, it could I thought you said you replaces that. I would replace the "switch" apart of the ignition switch. Let us know what happens. Here is how to change the switch out, also if this is not the problem I have seen the junction box on the passenger's side go out and can cause strange issues like this one. Check out the images (below). Please let us know what happens.