Turn signals do not flash when I use the remote-control key fob?

Does this car have an aftermarket car alarm? If so, the alarm has probably gone bad which is common, if you upload a picture of the key fob, I can tell for sure what kind of alarm it has. The wiring diagrams come with the alarm itself so we won't have those for you.

Yep, this is a factory alarm system for sure. There are three fuses #12 (under-hood) #25 and 30 (left side of dash) that run the system which need to be checked here is a guide that will help you and I have included the alarm system wiring diagrams below so you can see how the system works.

https://www.2carpros.com/articles/how-to-check-a-car-fuse

Check out the diagrams (below). Please let us know what happens.

It does sound like the alarm control module is going out, but I think we should check the electrical connector at the module to check for water damage or corrosion. Also, a CAN scan might be able to help give us a clue. You can get a CAN scanner from Amazon for about $30.00. here is a video to show you how:

https://youtu.be/u-4syLc-ifQ

Here is the location of the alarm module so you can check it out and report back. Also, we can try to reprogram the fob here is how.

Remote Transmitter Programming

NOTE
A maximum of four keyless entry remote transmitters can be programmed to the central security module. Programming must be done at the same time for all the transmitters.
To enter programming mode, first verify that the battery is fully charged, and the antitheft system is not armed or triggered (if equipped).

1. Turn the ignition switch from the OFF to the ON position four times within three seconds to enter the learning mode.
2. Turn the ignition switch to the OFF position. The central security module will remain in the learning mode for 20 seconds indicated by the LED in the instrument panel being illuminated continuously.
3. Press any button on the remote transmitter being programmed. When the signal from the remote transmitter is accepted by the central security module, the LED will flash.
4. To program additional transmitters, repeat step 3, with a 2 second delay after the LED flashes.
5. To exit the learning mode, turn the ignition switch to the ON position. If no transmitter signal is received by the central security module for 20 seconds, the system will automatically exit the learning mode.
6. Test all the programmed transmitters, by activating and deactivating the locking functions.

Check out A77. Check out the diagrams (below). Please let us know what happens.

If you honk your horn from the steering wheel, does it work? So, is it fixed now except for the beep?

If we out power to the alarm horn will it make noise?

I would have to say the alarm module must be bad. Here is how to replace it in the diagrams below. New keys will need to be made. You can also check the module for water damage. Check out the diagrams (below). Please let us know what happens.

That makes sense each system is a little different. Please use 2CarPros anytime we are here to help.