Can you bypass original wiring to start mower as the wiring is incomplete all I have is a ignition and a solenoid wires

dont bypass its a safety switch that doesnt let motor start if deck/blades are engaged

Your question is convoluted... is it a no crank or a no spark or both? Both, implies brake switch but can be other.

I find no detailed free wiring diagrams so I can answer only in general.

For engine crank, most ZTR mowers require brake ON, PTO OFF, and both steering arms OUT (ground drive neutral), then ignition switch to start position. Some ZTRs require operator in seat in addition.

As for spark... engine ignition kill shunt circuit will close to battery negative (frame ground) when ignition switch is in the off position, otherwise open at ignition switch. Safety circuits operate in parallel to the ignition switch.

When ignition switch is not in the off position, the following safety circuit conditions will close the kill shunt.

1. PTO on and operator not in seat.
2. Brake on and either steering arm out. (Most but not all ZTRs).

The incomplete diagrams I find show a relay that powers the starter solenoid so verify relay not energizing and trace back through safety circuits. A simple inexpensive automotive test lamp would be a useful tool for troubleshooting.

Starter solenoid activation is as follows;

Battery voltage is provided at the B terminal of the ignition switch via 30 amp fuse. When the ignition switch is rotated to the start position, power is applied to the ignition S terminal which is fed through 1 pole of the brake switch(on) then to a pole on the PTO switch (off) to the starter solenoid.

You can test the starter solenoid by jumping Red to White at the solenoid just be sure ignition switch is off and brake is on.

Wiring diagram

https://www.searspartsdirect.com/model/639ncgl4ue-000247/craftsman-917288515-front-engine-lawn-tractor-parts

ignition switch

there is 2 to 3 safety switches on there and any one of them will stop it from running. there is one in the seat, one on the engagement of the mower deck and one in the clutch pedal. some models also had an in-line fuse.

If it starts with the key when you jump it then it sounds like you have a bad or dirty connection in your battery cable or your battery is just too low. You didn't indicate where you were connecting your jumper cable, from the tractor battery or from another source. It could also be in your ground wire (but not if you only have to use one jumper cable). Remove the negative from you battery. Remove terminal from starter, and clean and be sure terminal is tight on the wire. Remove + cable from battery and clean. Remove ground terminal from engine, clean that connection. Check that the starter is firmly bolted to the engine.

Beings you can get to the solenoid I would check it first. There is a small post (not battery or starter), touch a jumper wire from battery to this post. Then with a test light check the wire to that post w/key in start position (remember you must be in regular start condition for this test). If no light, you can only go to each switch one at a time and bypass then try to start again. Not sure how many there are.

The large red cable from the battery should go to the large terminal on one side of the solenoid. The opposite side of the battery solenoid connection goes to the starter So now you have a heavy cable going from the battery to one side of the solenoid and another heavy cable (red) going to the starter connection. There should also be a small wire coming from the ignition switch to the small terminal on solenoid. If there are two small terminals on solenoid, ground the other one. To test the ignition switch, just turn the key and see if you get 12 volts, then you know that part is good. If not, check your ignition switch. So, back to the solenoid-----. If there are two small solenoid terminals with nuts for wires on the solenoid then the wires could be mixed up. So just reverse the two small wires and try again.

You would think they would make things easy and say on the solenoid, Battery connection here, and Starter connection here, and ignition switch wire here, but no, just nothing for the most part.

So now remember this is nothing more than a lightswitch type of a mechanism where instead of using your finger to flick the switch, we are using a small electric charge to momentarily close the light switch, in this case the starter motor, same idea.

I assume that you are jumping the solenoid in order to bypass an ignition switch that is no longer operating?

If so, did you have the key turned to the run position?

You should not need to bypass any safety switches, just be sure that everything is in the normal starting position. (deck disengaged, in neutral, etc.)

Either way, it sounds like you have a bad ignition switch, or faulty wiring between the ignition switch and the solenoid.

Either the igniton is bad or the wires are backwards. You can bypass the ignition and touch the wires together to see if the solenoid turns. You can also use an ohmmeter/voltmeter to check the current.