1999 Chevrolet Lumina won't Start

Wife drove to work fine, then went out to start car and nothing. Battery is good, but when you turn key to start nothing, lights go out on dash but nothing, not even a click on the solenoid. I put key in run position and jumped the starter and starter worked and car started, after starting it ran for 2-3 seconds and shut down. I tried both keys and theft protection light keeps flashing. I have read that there are two tiny wires that go up to the ignition switch, that if they break that it causes this to happen. Do I need to replace the switch or can I pull it out and fix the broken wire? Or do you think it is something else? HELP. PLEASE!