I am confident that your problem has nothing to do with compression, but while the subject is being discussed, if your engine has the usual B&S "Easy Spin" camshaft design, it is important to check valve clearance with the engine on top dead center. Easy Spin holds the inlet valve .010" open for something like the first half of the compression stroke, to make the engine easy to rope-start. B&S claim that it has virtually no effect at running speed because there isn't time for the gas to leak through with the valve lifted such a small amount. If you try to set valve clearance with the engine in the first part of the compression stroke, you'll end up with an enormous intake valve clearance on TDC. Some of the tappet adjusting techniques that work for car engines, don't work for B&S engines because of Easy Spin.
With regard to spark, I think you always need to check for spark with the black cord disconnected before you condemn the coil. Make sure the cord isn't touching anything anywhere along its length, too. It's probably a dead coil, but its very irritating (to me at least) to buy parts I don't need.
