When my radiator got a leak and the coolant got low, and mine did the same thing. If the fluid level is not high enough then I believe there is a safety feature built in that shuts off the engine.

Make sure you have plenty of antifreeze in there and have got the air out, by using the bleeder valve.

If the coolant level is too low it won't run. But if level is fine it will run even without the cap (at least until engine warms up). So you might try starting the car with the cap off to see if the level goes down quickly once you start it. The level should not change once started but taking the cap off once started might allow some trapped air out and allow you to fill it as needed.