I have a craftsmen 19.5 briggs and stratton mower, new battery, new solenoid, new brushes on starter all I get is a clicking sound. I have checked wires still to no avail.

I would first check the new battery with a volt meter just to make sure it fully charged, Seen new ones that were low.

Check all grounds on the battery/starter and solenoid.
Have you tried jumping the solenoid with a screw driver to take it out pg the loop and see if the starter is good?

Did you test the starter before you re installed it to make sure the brushes did the trick for the starter?

The clicking sound keeps bring me back to the solenoid. At this point test solenoid even though its new and check for good grounding there at all ends

Last but not least check for neutral positions in start position and safety switch grounding under the seat.

On a long shot if the brushes were bad and obviously as they were going bad the extra crank and amp draw there may have had adverse effects on the ignition switch..

Get back if you are still dead in the water Not much left in the link here except a bad flywheel problem and or miss aligned starter wheel. Since it's the old starter with new brushes then I doubt the wheel. The winding in the starter could have a problem also.

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