121518 Update: I just found out my links below weren't working. I'll see if I can get those fixed soon.
A potential fix for those mowers and tractors that are giving you the click at your start solenoid but are not cranking your engine over. Add a 5dollar relay circuit to activate your start solenoid.

Important: The process outlined here can be applied to 3terminal solenoids. It may be different for your 4terminal solenoids.
With a 4terminal solenoid, you need to be certain you're jumping 12 volts to the correct terminal. In this video, I do not talk about how to determine which terminal you should be jumping to. You could blow a fuse or even burn up wiring if you choose to jump to the wrong terminal. If you are not sure, then you should NOT perform the recommended test.

Disclaimer: I am not a mower or small engine professional. This video makes recommendations that could be potentially dangerous. If you are not certain whether you can follow the outlined procedures safely, then you should not attempt them on your own. Consult with a professional instead.

(Edited 2/2022) Link to Amazon for relay: 2pack is $8.99
https://www.amazon.com/ARTGEARHarnes...

Link to replacement terminals for Starter Switch coupler:
https://www.mouser.com/ProductDetail/...

Editor's notes:
The previous version of this video was unedited.
New battery=$25~$65
New solenoid (of this type): $85~$135
This modification: less than $10

Regarding Taryl's fix: Taryl is advocating for a different approach, which would require an additional 3terminal start solenoid and an additional battery cable. I would still endorse his method, though his solution would be more costly to implement. See his video here:
https://www.youtube.com/watch?v=8n2eO...

Netdoctor is from northcentral Ohio. Retired after 32 years working for a transmission manufacturing company.
Contact me at [email protected]

Disclaimer: I am not a doctor; I just play one on the Worldwide​ Web...