Why my emergency flashers work and my signal lights don't

Could be several things. But first make sure that the turn signal flasher is good. It is different than the 4 way/emergency flasher.

Check if your emergency flashers still work. You possibly need a new flasher. Some cars have separate flashers for turn signals and emergency flashers, but some they are both together. If your emergency flashers still operate leave them on and find the flasher (follow the clicking noise the flasher makes) and see if there is another flasher right next to it. swap with the emergency flasher and see if your turn signals work again. If so, replace the faulty flasher.

The hazard switch gets power from the horn fuse which is hot all the time, and from the turn signal fuse which is hot when the key switch is on. The turn signal switch gets power from the hazard switch and both use the same flasher.
So if the turn signals work but the hazard switch does not power the lights, and both fuses have power, I would say the problem is inside the hazard switch.

Check the relays and then check the wires... If its a relay you will need to replace it and of its a wire problem either fix the wires or get a new wiring harness

might be an inline fuse

you may have a blown fuse. that would be where i would look first.

since you know where the fuses are, you also know where the flashers are. the flashers are the same part so unplug the one for the emergency flasher and put it into the socket for the turn signals and vice versa. if the signals now work but not the emergency flasher you know to get a new flasher unit at any parts store. the flasher units are cubes about an inch on each side plugged into the fuse panel.

The flasher may have gone bad for the turn signal, and there may be a second flasher for the emergency flasher lights. Look and listen for a click of the flasher for the emergency flasher lights. Then, the other flasher is the one to replace.

Good luck on this repair.

there is a short in your liting system
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check if bulbs are burns