Is there a way to fix the the turn signal chime and other various chimes on a 2009 Chevrolet Cobalt LS, there is no sound from them as well as front speakers?

Just the left front (driver side ) speaker . Your best bet is to take it to a qualified repair shop. Radio blew a channel inside radio . An you can't just replace the radio with an after market one . This radio is connected to the GMLAN low speed data bus . If the vehicle loses radio connection it may not start . All the modules on your vehicle ,engine computer body control module ,air bags , anti-theft system ,anti lock brakes etc... Are on three different dats bus networks .
The communication among control modules is performed through the GMLAN high speed serial data circuit and the GMLAN low speed serial data circuit. The modules that need real time communication are attached to the high speed GMLAN network. The body control module (BCM) is the gateway between the networks. The purpose of the gateway is to translate serial data messages between the GMLAN high speed buss and the GMLAN low speed buss. The gateway will interact with each network according to that network's transmission protocol. Refer to Body Control System Description and Operation for more information about the gateway.

The powertrain control module (PCM) on this vehicle, uses a class 2 serial data buss. The class 2 buss is only used for diagnostics and the service programming system (SPS). During normal vehicle operations, there is no communications over the class 2 serial data buss. Normal vehicle operational messaging for the PCM is sent over the PCMs GMLAN high speed serial data buss.
Like I said your best bet is to take it to the dealer or a qualified independent repair shop. You have no idea of the complexity of your vehicle . Just the left front (driver side ) speaker . Your best bet is to take it to a qualified repair shop. Radio blew a channel inside radio . An you can't just replace the radio with an after market one . This radio is connected to the GMLAN low speed data bus . If the vehicle loses radio connection it may not start . All the modules on your vehicle ,engine computer body control module ,air bags , anti-theft system ,anti lock brakes etc... Are on three different dats bus networks . The communication among control modules is performed through the GMLAN high speed serial data circuit and the GMLAN low speed serial data circuit. The modules that need real time communication are attached to the high speed GMLAN network. The body control module (BCM) is the gateway between the networks. The purpose of the gateway is to translate serial data messages between the GMLAN high speed buss and the GMLAN low speed buss. The gateway will interact with each network according to that network's transmission protocol. Refer to Body Control System Description and Operation for more information about the gateway. The powertrain control module (PCM) on this vehicle, uses a class 2 serial data buss. The class 2 buss is only used for diagnostics and the service programming system (SPS). During normal vehicle operations, there is no communications over the class 2 serial data buss. Normal vehicle operational messaging for the PCM is sent over the PCMs GMLAN high speed serial data buss. Like I said your best bet is to take it to the dealer or a qualified independent repair shop. You have no idea of the complexity of your vehicle .