...while I had it I took an ohm test and it showed a resistance exactly the same as the coil I had. So I surmised my coil was good. and nothing was open or shorted out.
You can test a coil for shorts between the primary and secondary as well as the primary to ground and the secondary to ground. If you read a dead short (0 ohms) to ground from anywhere, the coil is bad. That's only the first step in the troubleshooting process though. A reading of "X" number of ohms above a short does not necessarily mean that the coil is good.
When I took the coil back to the mower shop and told him what I had done, He told me you can't check a coil with an ohm meter.. Did I just get lucky or is he mistaken?
The resistance of a certain coil should be within a specified range if it is good (i.e. 25 to 30 ohms, or 50 to 75 ohms etc...). The problem with this is that the manufacturers do not provide the information on what that range should be.
Yet another aspect is what coldone was talking about. Electrical insulation is ALWAYS rated for up to a certain voltage. The insulation on a coil winding keeps it from shorting from one wind of wire to the next. because the insulation of the individual wires in the primary and the secondary is physically touching inside the coil, the insulation must be able to withstand the highest voltage that the secondary will produce. as it ages, the insulation can loose some of its insulating properties and start to "short" between windings in an erratic way. It may read fine at the 9 volts that your meter puts out, but be intermittently shorting at 20,000 volts. There is a high voltage device that is used to test the integrity of motor and coil winding insulation called a Megger (Megohmeter), but they're expensive and not practical for the hobbyist to own. I hope that this answers some of your questions.
There's a lot of great information in this thread for someone who wants to learn.