I have a Murray 18hp Briggs & Stratton Riding Mower that won't start. The battery is good and the mower will crank without the (new) spark plug in, but seems weak. I thought maybe the battery needed a charge so I used a charger in the "start" mode and it still does the same thing. The relay seems to be good. With the plug in, the engine actually turns over once and then either the relay or starter starts clicking. Help.

If you check all the good stuff and know for sure that all the starting systems is good, including the starter, then I would start to look at compression being off. You may want to check the valves for proper adjustment.

Save yourself some agony and follow the directions do not skip one because "you have already done it" humor me and you will see the light.

You will need a volt meter and set it to DC volts
-Check the battery for 12.5 Volts
-Check the cables attached to the battery for the same voltage checking for good connections
-Attach the positive side of the volt meter to the + side of the battery and the negative side to the engine block, Still got 12 Volts? If not the ground from battery is bad.

-Now keep the ground on the negative side of battery
-follow positive cable to the solenoid and hook volt meter on the cable going TO the starter coming from the opposite side of the solenoid.
Turn key to "start" position you should have 12 + volts

YES-Check the same way on the starter motor where the cable FROM solenoid connects, If less or no voltage then cables or connections bad, If good voltage then starter is bad

NO- Take positive lead from volt meter to small wire going to solenoid and test for 12 Volts with key in the "start" position, If no voltage to small wire safety switch is telling it not to crank or ignition switch is bad (rare) If it does have voltage the solenoid needs replacing (common)

Hope it helps,
.Don