If you are familiar with the compression feel on similar engines (that use the same starter), then the weak feel is a useful clue. As you say, the decompressor is a likely problem area and should be swapped to see if it makes a difference. If you pull out the piston, remove the rings and measure the ring gap with them in the bore near the top. You should do that anyway if you are tidying up the engine, so it won't be wasted effort. Have you checked the crankshaft seal and bearing at the bottom of the engine? The roughness and noise you reported could be due to a failure of that bearing. If the bearing is loose and wobbly, the seal can't work.
Usually it makes sense to start by checking the spark and whether the engine will start easily if you prime it. We have tried to follow a shortcut by paying attention to the base engine before we look at the more common problem areas: the ignition and carburetion. It isn't a waste of time if you are going to keep the mower, because the base engine needs to end up in good shape anyway, whether or not the engine is running well when you check it.
When you report back on the current round of checks, please let us know what the spark looks like, whether you are using a new spark plug, and whether it starts easily if you prime it.
