Re: merc 4 hp single cylinder with issues
With all the wisdom of just one rebuilt Merc under my belt, I can add a few possibilities. (after all, I've done just about everything wrong at least once, the things that eventually worked for me might work for someone else)
You could try taking a very fine emory board (your wife will never miss it, she has dozens) and carefully clean the surfaces where the points come together (located under the flywheel). Get any and all dust and filings out of there. Set the gap to 20 thousandths of an inch as a good starting point, that's the setting for several small Mercury engines including my 3.9 hp unit from three years before yours.
Look to see if the ignition coil is discolored, cracked or shows signs having been exposed to too much heat. If any of those are the case, it will need to be replaced.
You can check for spark by grounding the plug (the bent over part) to the engine case (using insulated pliers and a rubber glove, plugs can snap at you) and having someone crank the engine. In any kind of shade at all, you should be able to see the spark jump.
Before you tear the carb apart (a different issue than ignition spark) try investing about seven bucks in some "Sea Foam", use 2 oz per gallon for a two cycle engine fuel mix. Also, if you can again catch your wife when she's otherwise occupied, borrow a perfume spray of hers, fill the spray with the "Sea Foam" and spray it into the air intake while the engine is being turned over. Magic stuff, "Sea Foam", often does the job of a carb re-build for you.
Gary