It may be in the switch?, I would look at the switch, see which way I am turing it (ususally to the right all the way over to start). Now go to the back of the switch and probe the connection that aligns up in the start mode and see if anything is going down to the solenoid? also inspect the wiring from the switch to the solenoid for chafes or bare spots or even a break? another way is to wire around the switch and go directly from the battery to the solenoid wire that comes in from the switch Not recommended unless you are familar doing this). IMO if it cranks by bypassing (hotwiring) with ignition switch then the problem lyes between the switch or switch it's self.

Fuse? In my experience on these, very few safety switches actually fail themselves, but fail to be fully actuated allowing them to work. IE the tab that hold the switch on the frame is bent and when the pedal is depressed it isn't quite enough. Try actuating the switches by hand and then cranking. Ignition switches do fail (as RC indicated) more frequently or the connections get rusty/ fatigued on the back. They are labeled as well for you troubleshooting pleasure. I have seen to where as the last person to have worked on it put the no mow in reverse wire to the single pole on the solenoid rather than the orange one...

Thank you both for the suggestions. I have been able to pull both switches off the frame so I will try making sure they are fully depressed, then try cranking it. I did replace the single 20 amp fuse earlier, but to no avail.

I did try jumping from the positive post on the battery to the small single pole on the solenoid earlier but nothing happened....

I will post back with results

I made sure the safety switches were depressed but still nothing.

I took the wires out of the harness that plugs into the ignition. There is a double-green wire (probably ground?) were the metal tip-clip is broken. Maybe this is the issue?

Unfortunately several wires popped out at the same time and now I'm not sure where they go on the ignition switch.

Parts Tree has an electrical diagram and the ignition module has the letters S,M,G,B near the electrodes so I should be able to figure it out. :)

Here is a link that might be useful: Parts tree electrical diagram

This particular model MTD has a habit of making an open circuit in the trigger wire (yellow) between the ignition switch and solenoid. You can diagnose this with a test light starting at the switch and backprobing from there go to the solenoid.

"I did try jumping from the positive post on the battery to the small single pole on the solenoid earlier but nothing happened.... "
I assumed that if you jumped the large solenoid terminals and it cranked that 1) the ground cable is connected at the solenoid mount and 2) the starting system- battery, starter, grounds, cables etc are fine. This being said and nothing changed would indicate your solenoid (new or not) said goodbye...

***"I did try jumping from the positive post on the battery to the small single pole on the solenoid earlier but nothing happened"***
That action should have elicited some response from a good solenoid if the solenoid is getting the proper ground it needs. Try giving the solenoid body a ground by clamping a spare piece of wire to one of the solenoid bolts with a pair of vise grips and touch the other end to the battery negative cable where it connects to the frame or engine. Then try the trick of using a jumper wire from the battery positive cable where it connects to the solenoid, over to to small post on the solenoid....no need to go all the way to the battery + post on the battery, it's the same "juice". Of course you gotta get that key switch issue fixed first now.

Thank you everyone for the responses. I'm going to go check the solenoid ground connections now.

I bought a new solenoid. I can't jump it either (from the positive terminal of the battery to the small terminal on the solenoid).

You guys are probably right about the ground connection, I just don't know what else to do to it.

The cable going from the negative terminal of the battery is bolted to the frame. I can cleaned (sanded) the cable and the frame then rebolted it and still nothing.

Again, I'm not an electrician by any means. My understanding is that the solenoid has one terminal receiving power from the battery, a second sending power to the starter and the third (small) terminal receives a closed circuit from the ignition switch (by way of the safety switches) which then activates the solenoid allowing the electricity to flow to the starter.

Does the solenoid itself need to be grounded? Is the mounting plate (when attached to the frame) acting as a ground?

"Does the solenoid itself need to be grounded?" Yes "Is the mounting plate (when attached to the frame) acting as a ground? " Yes
If the solenoid is grounded, and 12v is supplied to the small terminal via the ignition switch- then it connects the cables that run to the starter and + battery. When you jumped across the 2 big terminals and it cranked, that meant that the engine is sharing the same ground as the battery. The solenoid needs to be also. MAybe that is your issue. Touching 12 Volt to the small terminal would crank the engine from what we know- unless the solenoid is open or not grounded. Many times MTD will attach the battery ground to the solenoid mounting bolt.

Thank you tomplum! I had been working on the solenoid this whole time with it detached from the frame. I reattached it and got the solenoid to fire by jumping the small terminal.

Now I'm back to figuring out the sequence of wires on the ignition switch. I assume that G=Ground and S=Safety Switches? I don't know what M and B are for though.

How do I test the ignition switch itself? I know that two wires (an orange and a yellow) go to the clutch safety switch and from there a yellow/white and orange/black go to the deck safety switch and from there a orange/white wire goes to the solenoid.

Thank you everyone for the help! :)

Regarding the switch, I found a description for the switch on Amazon saying: B=Battery M=Magneto Kill S=To Solenoid L=Lights G=Ground

I have a 1996 yard machine

Starts up fine when cold but try starting it when it's hot it won't start till its cold again please any advice .I changed the plugs air filter checked the oil this is driving me nuts I just can't figure it out

Coil? This engine have a model number?

13AQ67OG372

Possibly has a Briggs opposed twin? There would be a number tag on the engine itself. If it is, fairly good money that the coil is culprit, or the vent in the fuel cap is obstructed. 590781 is the OEM number for the coil, though on this an aftermarket version may be better.