It sounds as if your new replacement spark plug had an internal short or breakdown in the center insulator. I think that is fairly unusual, though not unheard of. In the old days it was routine to check whether the ignition system would spark strongly across a sizable gap between the end of the plug lead and the cylinder head. A brand new magneto would often spark half an inch or a bit more than that. You should be sure to use the correct plug gap: if your "new" plug won't fire strongly across a 0.030" gap, throw it away - the basic Briggs & Stratton magneto service test requirement is double that.

Your broken HT lead probably didn't matter - it just sparks across the gap inside the lead as well as the gap in the spark plug. However it slowly burns the copper away on both sides of the break in the lead, so the lead fails eventually when the gap inside it becomes huge, so it's best to replace defective parts even if the engine is running satisfactorily.

Incidentally on multi-cylinder engines with Kettering (coil, capacitor and breaker points) ignition it used to be a standard mechanic's trick to identify and "cure" oiled plugs by running the engine and pulling off each plug lead in turn until you found out which one made no difference to the way the engine ran. Then you held that plug lead a quarter of an inch away from the spark plug electrode. The increased gap increased the firing voltage to a very high level, and burned through the oil fouling in the plug. After about five or ten seconds it would be running on all cylinders and you could put the lead back on the spark plug. I've used that trick myself - it works wondrously well, and is very useful when you're a long way from home when you foul a plug. (Most of us were way too cheap to buy new parts when you could get the old ones working again.)

I'll close this thread.