When the left or right turn signal is activated, the light blinks once then shuts off. When the hazard light is activated, it works perfectly with indicator blinking inside and lights blinking outside the car. Does anyone know what might cause the left and right turn signals to blink once and shut off? We're trying to isolate the problem. Thanks in advance.

I must have missed this at the time you posted it, sorry. The hazards and turns use a common flasher unit, with the turn switch diverting the output to only one side while the hazard switch sends it to both. Since the flasher is a thermal type and both turns don't work, the problem can't be south of the turn switch or north of the flasher unit. There are really only three things that could cause it:
1) A weak flasher unit that requires more current than normal to operate thermally. If that's the culprit then it's very likely the hazards would flash slower than normal.
2) High resistance in the "common" throw of the turn switch (basically a bad switch).
3) High resistance in the wiring or pin contacts between the flasher and the blinker switch, but not between the flasher and the hazard switch.