Capmbell35, Thanks for the post!! Especially the part on the valve adjustment. I own 3 Craftsman tractors and was having power issues on all of them. So far I adjusted valves on 2 of them and they now run like NEW!. MY 18.5 plowed through 5' high cow grass like it was not even there and no more bogging down. I too maintain my tractors very well and all have been VERY good machines. (FYI, the new craftsman tractors have lost their quality according to many reviews (2013)). The valve adjustment was simple (15 minutes). I would suggest adjusting the valves while engine is warm-hot. Adjusting procedures on the internet neglect to mention this. I include a link on how to adjust...... You saved me tons of money and time in trouble-shooting! Thank you again for posting and details on the fixes!!! Here is a link that might be useful: How to adjust valves on the B&S 18.5 Engine

If this engine has cylinders that are directly opposite each other, it is one of the opposed twins, a.k.a. "boxer engine". You might have a defective intake manifold gasket (piece of gasket shattered and missing) that is causing the dead cylinder to run too lean to develop any real power. You can test this with the engine idling by spraying a short burst of spray carb cleaner on the seam where the intake manifold joins to the head and listen for a corresponding increase in the idle RPM. If you hear an increase in RPM, there is a leak in that gasket.

Here is a little more information that might help clarify the purpose of the diode across the PTO coil (paraphrased from a Wikipedia article): The functional name given to the diode is a 'snubber'. Snubbers are frequently used in electrical systems with an inductive load (PTO coil) where the sudden interruption of current flow often leads to a sharp rise in voltage across the device creating the interruption (the PTO switch). This sharp rise in voltage is a transient and can damage and lead to failure of the controlling device (PTO switch). When the current flowing is DC, a simple rectifier diode is often employed as a snubber. The snubber diode is wired in parallel with an inductive load (such as the PTO coil). The diode is installed so that it does not conduct under normal conditions. When current to the inductive load (PTO coil) is rapidly interrupted (by the PTO switch), a large voltage spike would be produced in the reverse direction (as the inductor (PTO coil) attempts to keep current flowing in the circuit). This spike is known as an "inductive kick". Placing the snubber diode in inverse parallel with the inductive load (PTO coil) allows the current from the inductor to flow through the diode rather than through the switching element (PTO switch), dissipating the energy stored in the inductive load over the series resistance of the inductor (PTO coil) and the (usually much smaller) resistance of the diode. So, this inductive kick does not feed back into ground or into any other part of the engine such as the starter (as mownie correctly mentioned). The potentially damaging energy is dissipated in the series resistance of the diode and the PTO coil.

So I put the carb back together with the new parts from the rebuild kit and put everything back together on the mower. Started up fine and ran steady at full throttle. Tested low and medium throttle and seemed to run good. So I decided to take 20 mins to mow the front lawn and see how it ran. Everything seemed good while I was mowing, so when I got done I lowered the throttle to about half speed and it started surging again. Brought it in the shed, checked for good spark on both cylinders and ran engine on each cylinder separately. Fired it back up with both cylinders and ran fine at all throttle levels. Mowed the back lawn the next morning and no problems at all. Ran it at low, medium and high after I got done mowing and no surging. I am still a little concerned though because it did surge after the first mowing when i put it back together. Do you think my problem is fixed or is there something else I can check? The funny thing is my friends mower does the same surging when he runs at half throttle, but it runs fine at full throttle. He has a different model, but its a Briggs and has the same basic configuration. Is there a known problem that will cause these engines to surge when not at full throttle?