The problem is most likely the ignition lock cylinder, there are two tiny wires coming out of the cylinder that break over time. You can replace the ignition lock cylinder or you can bypass the system. If you want to bypass the system, use an ohmmeter to find the resistance across the chip in the key. Then go to Radio Shack and purchase a resistor of the same resistance value. Wire this resistor across the two white wires coming out of the steering column under the dash. These white wires are encased in orange insulation where they come out of the column, then break out of the insulation near the connector. See illustration below.
Is the ignition lock cylinder the reason that the starter remained on and burned out? or is the cylinder just causing the "pass key fault" theft lock?
Thats what I was thinking that the starter staying on was a starter problem. Alright thanks for all your help. Hopefully i'll get that fixed.