A quickie check which might give a clue as to the problem would be to pull the combination turn signal relay module. Then see what the radio does. (That is near the fuse box under the hood on my car - don't know where it is on yours.)

And check the fuse going to the radio.

Beyond that, I would check the voltages inside the car - like at the cigarette lighter. A low voltage can make electronic things act weird. Should be about 13/14 volts with the engine running. If it is like 11 or 10 volts, then that would be an alternator problem.

Then next I would pull the radio and check the wiring going to it - especially if it is modified from factory and do-it-yourself. Sometimes people "twist" wires together (rather than crimping) and there will be a "loose" connection over time. Maybe there is a loose power or ground connection going to the radio? And note there will typically be two power connections to the radio - one is always on and the other is only on when the ignition is on. Check those voltages as well. And then check with turn signal activated.