All batteries, even those using gel instead of electrolyte lose charging capacity as the time passes. The reason for this is that the chemical breakdown of the connections inevitably takes place leading to the deterioration of the plates and loss of the electrolyte. When your vehicle has start up or charging problems, the vehicle troubleshooting procedure should start with a test of the battery. You do that with a visual check followed by a voltage test. If the battery is ok, other components of the electrical system is probably the reason, but battery problems are by far the most likely reason.
If the car's dashboard battery light comes on, you might be able to make it home or to a service facility for a repair. The car will continue running as long as some juice is left in the battery, but if the charging system isn't working or you have a bad alternator, your car's engine will stop running once the battery is drained. If you turn off the engine, you won't be able to restart it if the battery doesn't have enough charge left to power the engine's starter motor.
Starter: starting the car was a sweat-breaking business before the starter. A procedure by it's own, where you had to be fairly skilled. Cranking the car was done with a cranking rod. The driver would put it into place, use all the strength available, crank the engine and if he's lucky the engine would start after a few turns. If not, he was in for another lesson in body-building. Aside that, when the engine started the driver had to let loose of the rod in time or else he would get a knock in the face. Every time you put the key into the ignition, remember this and enjoy it as a privilege.
With other electrically powered features, the cause (and the fix) may not be so simple. Because of that, if any electric accessory stops working it's a good idea to first check whether a fuse that protects the circuit it's on has blown. The owners manual should show where a fuse for a particular feature is located (usually in a side panel below the dashboard near the driver's seat or under the hood). If you're handy with a multimeter that measures voltage, resistance and other things, you may be able to diagnose some of your own electrical problems. However, because they can be difficult for professionals to find and fix, they might be even harder for amateur technicians to solve.