First time driver here, got my licence quite recently. I'm driving my Mom's Renault 19 this week, but today, the indicators stopped working. More exactly, they work when the engine is not running, but they don't work anymore when the engine is running (don't work = no feedback on the board (light nor sound) and the lights don't light up). BUT the hazard warning lights do work no matter the condition! I'll precise that today was a fairly cold day in France, the engine may have been humid / cold. Also, the car made a noise it does not do otherwise during the trip, like a turbine. It's a little vague so I'm not asking an idea for that one, but may be it's related.
The hazard lights in every car I've ever drive work whether the engine is turned on or not. The turn signals (indicators) work when the engine is turned on. It sounds like something is interrupting the power going into the turn signal switch when the engine is running.
One possibility is that the alternator isn't working and so the engine is lowering the overall system voltage such that it doesn't have enough power to energize the turn signals when the engine is running. I'd try cleaning the electrical connections going to the turn signal switch. I'd also make sure that the alternator is working.