Looks like this:
Generally is found on the under part of the motor, the hot and ground wires are usually visible, as the crank is pushed up against the flywheel internally. The click does sound like the starter.
That would be where I start my repair efforts. Good luck with it. Starters can be tricky, they come with shims. Usually you can just use the shims that are already there, but if for some reason you can't, use the new ones exactly like the old ones...(ex. if there were 2 shims, use 2 new ones assuming they are the same width).
Make sure you disconnect the battery first.
-- Bill