Replaced the ignition coil on an M-Series Lawnboy. Wire was frayed.
Now I am having a hard time starting it (and I was having troubles
before I replaced the ignition coil, so I might have had more then one
problem). When I pull the cord, absolutely nothing happens.

I do get a spark, so that is not the problem.

I wonder about the compression. According to the repari manuals I've
read you are supposed to test compression by putting your finder over
the spark plug hole. It should blow off when you pull the cord. Mine
does not. And when you turn the flywheel counterclockwise it's
supposed to recoil in the opposite direction if your compression is
good. Mine does not. However, on the other hand, another manual said
that your compression is good if the pull on the cord is uneven, which
mine is. So then I wasn't sure. Can anyone give any further insight
on how I would go about trouble-shooting this problem?

What might be most telling is the fact that sometimes when I pull the
cord the engine backfires. Is that indicative of anything?

Thank you for your time,
Brian