Tim, have you checked fuse #3? Power for the hazard flashers is through fuse #6 and the turn signals are powered by fuse #3. The reason for this is that the hazard flashers work with the key switch OFF. The blinkers only operate with the key switch turned to ON. Therfore, fuse #3 gets power from a bus that is powered through the key switch, but fuse #6 is hooked directly to the battery and doesn't go through the key switch. Both the hazard flashers and the turn signals use the same flasher module. The flasher relay feeds into what is called a NASO Hazard/Turn Signal Converter. This is just a fancy way of saying it's a device that senses whether the hazard switch is pressed and needs to blink both signal lights or if only the blinker switch is working and for which direction. The blinker relay is cheap, but the NASO converter is expensive. Probably you don't need either.
I'm guessing your problem is the fuse #3 or the turn signal switch. Fuse #3 is only used for the turn signals and a rear worklight if installed. If it is blown, you will see exactly the symptoms you described. Have you removed your instrument panel by taking out the two phillips head screws? Lift that up after removing the screws and the fuses are on the left side of the cutout area.
If you check fuse #3 and still need to get to the back of the turn signal switch, you'll have to remove the black cowling on the left side under the steering wheel and dash panel. To remove it, you remove the two bolts just below the steering wheel and then there are two more bolts you have to remove on the back side of the firewall. Lift your hood and look in past the muffler to the firewall area. There are three bolt heads there, but you only need to remove the lower two (a ratchet with long extension is needed). The top bolt holds the top of the blue dash in place. Once you get that cover off, you'll see lots of dust. Use a soft brush or compressed air to remove any dust if you want, but DO NOT wash this area with water. If it gets wet in there around the relays, you'll have all sorts of problems until it dries out.
With the cover removed, you'll be able to get to the back side of your turn signal switch for examination and testing.