I think the same thing. Let me be as detailed as I can to be sure everything is understood.
I bought this with swap mostly done. I was told the engine and trans were done together. After finishing connections and obtaining missing coolant reservoir and air intake. I filled with correct fluids and rotated motor by hand to verify it is not seized. Then tried starting. With key: if I tried normal speed I would get nothing. If I did a fast rotation with key I would get a single thunk. I could jump pins in the relay and the engine would crank, start and run at high idle for 2 to 3seconds then die and not repeat for a couple hours. I tested the starter and circuits and found wiring (trans harness) that needed repair. After that I got nothing at all from the key and cant jump the relay anymore. Now when I jump the relay it just cranks. Inspected wiring, and circuits. Again I found wiring (engine harness) and repaired it. Now I charging the battery to continue testing.
It did seem like cutting off when it did start due to an immobolizer. But, keys are black, nothing in column for SKIM, and nothing under dash that looks like system drawings in FSM I got from the boards here. So either remove and ignition replaced, wear on keys contradicts that, or it is not supposed to have SKIM.