what should i look for when my blinkers and hazzard lights quit working on 1998 Chevrolet Cavalier

already replaced relay switch for blinkers

Asked by for the 1998 Chevrolet Cavalier
I assume you have checked ALL the fuses?
yes all fuses look fine have even replaced them to make sure
MOST likely the combo. or signal light switch is defective. This switch is also the hazard light switch, as well as other functions. That is why it's called a combination switch.
1 more answer
Well: the circuit, the bulbs, the fuse, the relays,the switch itself.The sockets that the bulbs are in could be corroded: remove the lens to see if corrosion is present and if the bulb is dark,which means it is blown, and I would replace all the bulbs while I am at it because they tend to blow close together.the switch could be worn and loosing contact inside. The circuit wires could be short-circuiting somewhere .Use diaelectric grease to pre vent corrosion.