Crazy Ignition Issue

Sounds like a bad ground somewhere, the run position on the ignition swich is losing power once the car is beyond the initial startup. Bet something was disturbed during the R + R, like a wire was pulled out of a connector just a tad or is now in a place it wasn't befrore. Did you check the 'run' circuit fuse?

Got a muiltimeter? Hook it up to the switch if you can and watch for voltage drop when the switch is in different positions. Trace the circuit with the meter until you find the problem area.