Nice looking 'vert fella, schweet.
ironically, on the recent TopGear with 3 e30 convertibles, the easiest to start and steal was Hammonds with exactly the same BMW immob. as you.
One item I would check is behind the glovebox panel, a two pin connector with green wires. If the wires disappear into the loom... just remove connector and jumper the two pins. the green wires are the feed for the ignition.
Heaps of e30 experts in Melbourne...