To enlarge on Phil's recommendation, remove the battery, then unbolt the black lead (-ve) where it attaches to the chassis together with a small bracket to hold the battery. I suspect you will find corrosion there, leading to high resistance. Clean both the spade connection on the black lead, and the chassis (you may have to remove paint first with a file, abrasive stone, etc) with emery paper until there is a good, bright metal-to-metal contact. Lightly skim the exposed metal with Vaseline or light grease to prevent corrosion, then bolt the spade terminal with the battery bracket on top (so that is spade directly to chassis) and tigheten firmly. If your new battery is fully charged, the starter solenoid (the thing that is clicking) should operate properly, and the engine should fire.
Corrosion on the black lead-to-chassis connection is a common fault, and stops sufficient current flowing to operate the starter solenoid, even with a fully charged battery. You should check this at the beginning of each mowing season.
JD, July 2008
