Next check the turn signal switch inside the steering column. check to see if the bulb is dead
The most probable answer is that you have a bad flasher.
I had the same problem in my 1999 Mercury Cougar, I replaced the flasher located in the blinker assembly. It was very simple to do. Flasher cost about $10
Blown fuse or bad flasher unit. Often, cars use different flasher for the turn signals and the flasher, so it is possible for the hazards to work and not the turn signals.
you may need to replace the flasher relay it should be in the fuse panel
The fuse for the blinker of a 96 Cavalier should be in the fuse box inside of the car. A more likely cause would be the flasher, located under the drivers side of the dash.
both left and right blinkers operate off of the same flasher. the flasher is a small module that plugs in usually under the dash just above your left leg as you are sitting behind the steering wheel. a bad turn signal bulb could also cause the dashboard indicator light not to blink.
A burnt out signal bulb, a faulty blinker relay, a faulty blinker switch, a loose connection or a broken wire are all things that can cause the turn signals not to operate properly.
Check the Flasher, its usually located under the dashboard on the drivers side. its the thing that makes the clicking noise when you use your turn signals. Go to your local auto parts store and tell them about your blinker not working, they can help you get the correct flasher and tell you where its located. Be aware some vehicles have two of them. If this isn't your problem, make sure all your bulbs are good, all the fuses are good and if that doesnt work call a mechanic because it could be the blinker stalk ( the thing you pull on when you use your blinker) or a wiring problem
A bad ground wire is the most common cause of turn signals and brake lights not working. The ground wire connection might be corroded.
turn signals and emerg flashers work off a flasher can. go to any auto store and buy a new one they are cheap and easy to replace
Try replacing the flasher relay.
I have a 1996 D R and have the same problem. Apparently the flasher switch needs to be replaced.