1996 Mercury Sable 1996 Turn and Hazard Signals not working

At the applicable fuses, did you use voltage tester at the fuse circuit to check for voltage. The hazzard fuse should be hot all the time. The turn fuse may go hot when you turn on the key. You may have to check the multifunction switch?

I know you said you replaced the switch, but did you replace the little can up on the steering column that has two wires coming out of it? There are two of them located up on the column behind the dash panel. If that relay is junk (i.E. Melted together inside) you won't get any flashing. Or it could be just disconnected. Before doing a bunch of wiring get a $6 part at Autozone and change it.

Oh and a word to the wise. There are two of them. One is for turn signals. Put the car into "on" position and test you turn signals, and feel the "tink-tink" sound coming from one of the little cans. The other one is the hazard flasher can. Nothing like replacing your turn signals when you didn't have to.