I have the same car with the same exact issue. New Bulbs, new relay, and new fuses, wether they needed to be changed or not. Still no luck. I did however notice that the signals work intermittantly when I mess with the hazard switch on the column. It appears from the service manuals that the turn signals and the hazard switch are in an all inclusive module. This may be a possibility, but I cannot confirm this right now.

The Ford Taurus Owners forums indicate that the turn-signal lever switch (multi-function switch) commonly fails on these cars.

The part is about $80 and takes about 1/2 hour to replace.

Good luck.

Check all bulbs for one (or two) that's burned out. This will stop the turn signals from operating as well as the hazard lights.