This is another one of those questions that goes "I did everything right, but it doesn't work." If everything were right, it would work. You need to find what's wrong.
You find what's wrong by systematic troubleshooting. First, see if you have spark at the top of the coil--crank the car with the wire end close to the block, and you should get a bright spark. If so, the points, coil, and capacitor are OK, and you need to look at the high-voltage bits. If it doesn't check out, disconnect the coil from the distributor, and connect an ohmmeter (you do have a multimeter, right?) to the distributor wire. You should see the resistance change from zero to infinite as you turn the engine. If not, something is set up wrong with the points.
Keep eliminating things in this way, and eventually you will locate the problem.
Oh, and yes, if the ground wire from the plate is broken, it COULD cause what you are seeing, or maybe not. But the troubleshooting methodology should rule this in or out pretty easily.