I connected an ignition coil to 240v in an attempt to make a Hv generator. The ignition coil was connected I series with a capacitor and light dimmer. When turned on the ignition coil did nothing at all. I think this means it had an open secondary coil... this is supposed to damage the coil. Somebody tested the coil, and said it was fine. Should I be worried?
I have used a dimmer switch in series with a capacitor on 120V mains many times to drive an older style ignition coil. There were plenty of instances where I had the spark gap too wide, but did not damage the coil. Generally you should only be concerned if you run it for an extended period of time. It can cause breakdown within the coil which will lead to permanent damage. However, if you only had it running for a relatively short time, and especially if the test technician said it was fine, then no, I don't think you have anything to be worried about.
I recommend looking into your circuit to determine why you didn't get a spark. It could be as simple as your spark gap was too wide (try at around 5-10 millimeters, for most coils). It also could be that your capacitor has too low of a capacitance (try 1-2uF), or that you need to adjust your dimmer switch a bit until you find that sweet spot. As I mentioned in the comments, the dimmer switch "chops up" the mains sine wave so that it has relatively sharp edges:
The application and sudden removal of current from the primary winding in the ignition coil causes the voltage to spike substantially, and this in turn induces an even higher voltage on the secondary coil. However, if the "pulse" applied to the primary coil is of the wrong shape (dimmer knob is not adjusted to the right position), the voltage may not be removed quickly enough to generate a spark at the output.