My old lawnmower was not a Honda but a couple of problems and solutions that I had.
As it aged it became harder to start. I found that taking the float bowl off each spring and gently bouncing the float up and down will letting fresh gas flow through really helped. I think I would have burned it to the ground long before now if I had not been told this trick by my brother.
A couple of years ago it just would not start. It had fresh gas, plug had spark, appeared to have compression, clean air filter and every once in a while it would fire and give me hope. I was prepared to buy a new mower. Having a beer with a friend and was telling him my mower woes....... He said, simple engine, it can't be tough, bring it over....... So i did, he did a few simple checks and didn't find anything and sent me home with his mower to cut my lawn. It wasn't long before he called...... The shear pin on the flywheel on the top of the engine had been sheared. With the timing running off of the flywheel and the flywheel no longer connected to the crank it would not run. A new shear pin and I was back mowing.