If it starts but doesnt run when the key is let off, its not getting Ign 2 power. I have no idea what could be going on with the turn signal affecting it. Look at the base of the column for a long flat connector. Check that for burnt wire, wiggle it around and try starting again. Pay close attention to the yellow wire, it likes to burn.
If the car has a ballast resistor, check that. Engine dying when the key is let off is an indication that the ballast is bad.
