The starter draw is too much for the k38 contacts to handle , but they will handle the low draw of a test lamp or meter.

My suspect is the k38 and the cluster has to be pulled to get to it.
The terminals you want to jumper there are 1 & 3, which are relay terminals 30 and 87.

That will eliminate the K38 from the starter circuit.

You also have a ATA problem that may or may not be the reason for the K38 not working, but that is another story. I still would recheck all fuses to see if you can get the LED ARM lamp to come on..did you check the other ATA fuses I mentioned?

I also would like to be sure your battery is up to full charge.

Most guys that have ATA failure just jumper the k38 permanently by soldering a jumper across the K38 terminals 30 and 87 on the relay and plug it back in and be done with it...you only loose Alarm starter interlock.
If relay does not do the trick, check the ignition sw,...I have another test for that.
The power goes from bat+ to ign/sw, to K38, to NSS , to X27, to starter......just for your info on the series chain logic...any open circuit/contacts/poor connections in that chain results in no power to starter.

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A Dalton