Just a guess, but an ignition switch supplies the ignition with 12volts in both the run and start positions. Your ignition may be getting power in the start position but losing it in the run position. Check to make sure you have power to the ignition in the run position. If not could be a fuse, bad connection, bad ignition switch, etc. An electrical schematic should tell you which wires out of the switch should be hot in run. You could always supply the ignition with 12volts with a jumper wire to the battery post and see if she runs.
BUILT FORD TOUGH