It's beginning to sound like you're dealing with a bad condenser. "new" doesn't necessarily mean "good" and it takes a tester most people (not even me) don't happen to have handy. Try disconnecting the condenser temporarily and see if the coil, not the points, starts sparking. The condenser is there to protect the points, but it won't hurt to cycle them a few times without it connected, for testing purposes.
Jerry