I took the solenoid out of the mower and got a replacement for it at a local auto parts store, installed it and the mower starts now. However, the starting is a little labored, kinda like the battery is weak. It's a brand new battery, but I read on this forum that it would be a good idea to put a charger on the battery to make sure it is at full charge.
On the condition that the battery is already fully charged, does anyone have an idea why the mower is hesitant to get started. What I mean by this is that the flywheel is slow to turn when I first turn the key. Once it starts turning, then the mower starts pretty easily.