So all I have connected are the battery, alternator and starter cables, along with the ground stud in the side of the block. I went to connect the battery today and the motor instantly turned over. I don't have the grounding straps or the positive battery junction connected. So is there something amiss in the starter/alt/battery connections, or would not having everything else connected be causing this?

 

Sounds like the purple wire lug on the solenoid is touching on the battery cable lug on the solenoid.

 

Sounds like the purple wire on the starter that comes from the ignition is getting 12v constant. check if the 12v (big wire)from the battery has been jumped to the purple wire on the starter (small wire)

 

Did the same thing. Need to loosen the the wires and make sure they aren't touching.