A bad gas cap could cause your check engine light to come on but a bad gas cap cannot cause your car to not start.
As long as your fuel pump is pumping fuel and giving enough fuel pressure and your car has spark then it should start.
If not then you need to check the fuel pump for fuel pressure, bad fuel injectors, ignition coil problems, bad spark plugs etc.
But the gas cap should not cause your car to fail to start but like I said it could cause your check engine light to come on if it's not sealing properly.
A gas cap should really easily last at least the life of the car and you really should never need to replace a gas cap on a car or other vehicle.
But sometimes they might fail after 10 to 15 years of taking it off and putting it back on and then it might not seal properly.
Manufactures say gas caps on vehicles should last 50,000 to 100,000 miles but I've had gas caps on 30 year old trucks that were the same one and never needed replaced.
Usually I trade in my vehicle before the gas cap ever fails.
I've personally never had to replace a gas cap and they've lasted just as long as the car has.
A gas cap could go bad though and not seal properly so if the gas cap is not sealing correctly and causing your check engine light to come on then it would be time to replace the gas cap.
A gas cap should last 50,000 to 150,000 miles or more according to some manufacturers but usually gas caps last as long as the vehicle.
You can however replace your gas cap with a locking gas cap which would be a good idea to prevent gasoline theft from your vehicle.
If your check engine light comes on and there's no other issues and you've tightened your gas cap enough and the check engine light is still on then it could be your gas cap.
A new gas cap is pretty cheap as well though so it's worth changing it out and I would recommend if you're buying a new gas cap to buy a gas cap with a lock.