Immobilizer module lock out

I went to jump start a neighbor and found out someone attempted to steal my van. Steering column was open, and the lit up ring that is around the ignition was taken off and hanging down. I tried to start the car to do the jump anyway, and deal with the mess after. Car started for a second then shut off. This happened three times, and on the fourth attempt, it did nothing. I found out after researching, that the ring was part of the immobilization module, and since it did not read my key in three tries, it locked me out.

I put the ring back around the ignition, since it was still connected with the wires it hung by, and still lit up, but it did nothing. Tried a few 'reset' attempts to no avail.

The black box, and ring portions of the module, individually appeared to have no damage, and it seemed like they work, as I was locked out of the system seems like they did their job?

The plastic arm, that connects the box, to the ring was broken, resulting in two pieces.

My question is, would that bracket being broken effect the signal traveling from the ring to the unit? Does the solid plastic arm/bracket, have anything to do with the module's performance, other than mounting it in the right place?

It seems I should be able to have the module reprogrammed to accept my key again, and it is fine, but the shop I took it to said since that bracket was broken they could not reprogram it, and needed to order a new one. I have asked multiple times if they would at least attempt to reprogram it, and I am fairly certain they have not even tried yet, just keep saying they cannot because it is broken.

How does this module work? Microscopic fibers integrated into the plastic of the bracket?

Thanks.