Okay, that isn't good. Without the key in the start position there should only be a single hot terminal that comes from the battery and when the relay closes it then sends power to the starter. The other two will be the control side of the relay and it seems the ground side has shorted to power. That is why it won't start with the key, with battery voltage on both terminals they cancel each other out and the relay doesn't trigger. So, we need to find the ground wire, it is black and should go from the fuse and relay center out to a ground connection at the right front of the engine block. It is the ground in this diagram. It shares that ground with multiple other items, one of which is the transmission position sensor.
I would find the bolt it connects to, then remove it, now test to see if you have battery voltage on it, if you do go to the items indicated and unplug them and see if one of them is shorted to power first. Like the AC relay, the brake light relay, the O2 sensors, possibly one of those got pinched when the engine was reinstalled.
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Monday, April 10th, 2023 AT 8:26 AM