The recommended way to check compression with a B&S engine is first and most important, disconnect the sparkplug, then reach under the mower base and turn the cutter plate backwards until you feel compression, then see if you can bounce it off the compression pressure: flip it backwards and see if it rebounds. If it does, compression is OK. (This is considered better than just feeling the compression on the start rope because of B&S's remarkable compression-ruining camshaft design, but with a small amount of practice you can feel it on the start rope anyway).
Because you have apparently partly dismantled and reassembled the engine, the number of things that might be wrong with it is now much larger than it was before you did that.
