My 2008 Chevy Cobalt coupe has a passenger side turn signal that flashes fast on the instrument panel. However, no turn bulb is burnt out in either the front or rear. The rear passenger turn blub just flashes fast while the front passenger turn bulb just stays lit but doesn't flash! On occassion, the hazard lights will not turn off while the car is running and just flashes. Is the flasher broken inside the hazard switch, do I have a defective body control module or is it something else?

change the front bulb

Buy a two pack of turn signal bulbs. Change the front and rear left bulbs and try it out. If you're lucky, you're done and got away cheap. If not, start chasing electrons. Not an overly complicated circuit, the signal is quick flashing because you have an inoperative lamp.

Check you bulbs first because a bad bulb will cause this also !

Take it to a qualified repair shop

Just exchange the rear signal light bulb for a new one, that will fix the problem Ps, it will be wise to replace the one on the other side as these bulbs have a life expectancy, do them both at the ame time.

you need to get a two wire socket that matches the old one exactly.

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

The socket is likely burnt,or broken wire in the circiut

No - headlight ok.
The reason that the Right turn signal blinks fast is that there is half the normal load (resistance)
on the right side, since the Right front turn signal isn't working.
Since you replaced the Right front turn signal bulb, your problem lies in the bulb socket or
the wiring to the socket.
(1) try cleaning out the socket - there's probably a contact problem in the socket. You
may need to squeeze the contacts together to provide good contact to the socket contact.
(2) if contacts inside the socket are ok, try back-probing the socket - to make sure that the
socket is getting 12V DC to light the bulb. Replacing a bulb socket is easy, and commonly done.
Any auto parts dtore should be able to sell you a new socket - its just a matter of cutting out the
old one, and then splicing in the new one. Most shops will use small wire nuts, buried under several
wraps of E-tape (electrical tape).
(3) if bulb AND socket ok, you have the worst problem known to man - a wiring fault. In this case,
you'll want to run a new wire from the flasher module (under the dashboard) to the turn signal.

Replace the burned out bulb. It is flashing fast to alert you that bulb is burnt out. Turn on the side that works properly & note all bulbs flashing in front, rear & side. Most likely there is at least 1 burnt out on the other side.

replace flasher......usually located in fuse block area...listen in this area....select passenger side ...then select driver side...you can hear flasher clicking...you have seperate flashers for each...FLASHERS are small cubes plugged into fuse block....probable bad driverside flasher