Its unlikely you installed the cap and rotor wrong. Its possible that the cap or rotor (more likely the rotor) was the problem. It wouldnt be the first time a faulty part has been sold. If the rotor actually "broke" it would cause the engine to just shut off.
Im a little leary of the labor charge, especially if most of it is for diagnostics. Its just not that complicated to tell if an engine isnt getting any spark, and if its not getting spark, its not running, theres not much "diagnostics" that can be done to an engine thats not running.
Whenever you take a vehicle to the doctor and they tell you they replaced a part, demand to see the part that was removed. Theres no telling what was wrong with it now and theres no way for you to prove it wasnt the cap or rotor. Lesson learned for $210, its cheaper than college.