I have a older model mtd riding mower model 132-669G062/95186,my issue is it wouldnt start it ran fine when i put it away last year,so i replaced the battery,solenoid,and ignition so far and still nothing it will click once then thats it.It will run if I take jumper cables and hook up to the positive on the battery and touch the starter it fires right up and runs great just wont turn over with the key.Any help is appreciated thanks.

Look for a corroded or loose wiring connection.

clean all your power cable connectors

Search for a consumed or free wiring association.
clean the entirety of your capacity link connectors, use oil in every connector.

When cleaning fails start doing point to point voltage drop tests on the starter main and trigger circuits. Remember these circuit must be activated for these tests to work.
 
Things like bad crimps on terminals and loose fitting terminals can cause this problem. I have seen both over the years.
 
I had customer that changed starter, voltage regulator, and stator to no avail. Finally gave up and brought the mower into my shop. Upon doing voltage drop test I found a hinge spring on a F56 terminal at the ignition switch.
 
I also had one case where the terminal that fed power a mower's ignition switch where only one strand of a multi-strand wire was making contact. The voltage would only drop out upon the starter relay being triggered.
 

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A lawn mower is not a machine that you use frequently. So, it is very likely that it might not work properly immediately after you start it for a long time. If you are having difficulties getting your lawn mower to work, the humidity of the storage environment is often the cause. for more info

Have john deer Z225 EZtrak Has 18.5 hp briggs 0146-G1, mower won't crank , have replace ingnition coil ,tested bad new coil test 10.31 across , replace sollenoid , starter check good . fuses are good , new switch , yesterday went from battery to starter direct with key in run position , started and ran , today will spin but now no fire ,replace plug still no fire , re gaped coil ,no help. at wits end , any help would be appreciated. tomorrow if not raining will pull switch and test it, it's new but still could be bad.   turn Key to start position no noise, been a while since i ran the valves , but don't think that would keep it from firing, will be looking at switches next, would help if I had good wiring diagram  Thanks in Advance , Art

Your post is somewhat confusing.
 
What is it currently doing now? 
Does it SPIN over, does it have spark when /if it does?
 
Will direct 12 volts to the starter lug crank/spin it over? 

It sounds like you've already taken some proactive steps in troubleshooting your mower's starting issue, but I understand the frustration of still encountering problems. From your description, it seems like there might be an issue with the electrical connection or the starter itself.
Here are a few additional steps you could consider:

1. Check Wiring Connections: Ensure all wiring connections, especially those related to the starter, solenoid, and ignition, are securely connected and free from corrosion. Loose or corroded connections can prevent proper electrical flow, leading to starting issues.
   
2. Test Starter Relay/Solenoid: Even though you've replaced the solenoid, it's worth double-checking its functionality. Use a multimeter to test if the solenoid is receiving power from the ignition switch when you turn the key. If there's power but the starter isn't engaging, the solenoid might be faulty or improperly installed.
   
3. Inspect Starter Motor: If the starter motor isn't receiving power from the solenoid when you turn the key, there could be an issue with the ignition switch or wiring. Additionally, check the starter motor itself for any signs of damage or wear that might be preventing it from engaging properly.
   
4. Voltage Drop Test: Perform a voltage drop test on the cables between the battery, solenoid, and starter to identify any excessive resistance that could be hindering the flow of electricity. High resistance can cause voltage drops, resulting in insufficient power reaching the starter.
   
5. Consult Manual or Professional: If you have access to the mower's manual, refer to the troubleshooting section for specific guidance on starting issues. If the problem persists despite your efforts, consider consulting a professional mechanic or technician who specializes in small engines or robotic mowers. They may have the expertise and tools to diagnose and resolve the issue more effectively.
   

I hope these suggestions help you pinpoint and resolve the starting problem with your riding mower. Don't hesitate to reach out if you have any further questions or need assistance. Good luck!