Dashboard lights flickering and the car shuts off

The first thing I'd check is the alternator, because those symptoms of flickering lights and stalling at traffic lights usually point to the battery not charging while the engine's running. The cables might look fine on the outside but the alternator could be failing internally, so you need to have it checked with a multimeter to see if it's putting out the right voltage. It could also be a loose connection on the battery terminals or a cable that's corroded on the inside, so before you spend money on a new alternator, have someone inspect it properly with tools to rule that out first.

Have you tried starting the car with the lights off to see if it keeps happening? Because if the alternator isn't charging, the battery drains quickly, but it could also be a loose connection at the battery terminals that you can't see at first glance - sometimes corrosion gets inside the connector and you get that exact problem.