Jump onto www.toro.com and download the free service manual for your machine. Note down all the details on the ID plate on the mower, you will need it to find the correct manual......
From there you can get the part number. Good Luck!
Back firing could be an ignition, or valve timing issue, also check the function of the anti fire solenoid on the bottom of the carb float bowl ( you should hear this click as the ignition is switched on) you can also remove it and watch the centre pin retract when the ignition unit is switched on, next thing to check is that the flywheel key has not sheared, this will involve removing the flywheel, failing this remove the rocker box cover and make sure both valves are moving freely as the engine cranks, it could be a stuck valve.
Sounds like you may have stripped the thread in the head when retightening the new plug :( Can be repaired by using a helicoil, however, quite likely, the head will need to be removed to do so to ensure no junk falls into the cylinder.
Disconnect the negative battery cable.
Raise and safely support the vehicle.
Remove the drive belt shield at the right wheel well.
Remove the drive belt.
Remove the drive belt tensioner mounting bolt.
Remove the drive belt tensioner.
https://www.ronmowers.com/brand/toro
I have found that although they may look similar, with out changing brackets and adding new pulleys they will not interchange. Also decks from the same manufacturer will be different in different years.
Kohler EFI trouble chart.
Suggest you replace spark plugs and air filter if you haven't recently. Check for water in fuel. There is another fuel filter in the EFI system but not likely your problem.
The safety interlock system is designed to prevent the engine from starting unless: • The PTO is disengaged. • The motion control levers are in the brake position
You have to check both arm switches and PTO switch. AND somewhere/how there's a automatic park brake switch but I'm not locating in assembly drawing. If I've got the right model, you should hear the automatic brake deactivate when you pull both arms in and then set brake (default) when levers pushed out.
Make sure nothing is interfering with auto-bake. Once all the interlocks are satisfied, rotating off/run/start switch to start will energize starter solenoid.
Operator and service manuals available free from Toro.
https://www.toro.com/en/parts/partdetails/?id=27013
You should be ok to clean the carburetor out clean the gas tank out and put new spark plugs or clean the plugs real good and it should crank be sure to run clean gas through line to fuel pump to be sure of gas circulation
Try starter fluid to determine whether its a fuel problem or spark. Remove air filter cover and filter and spray a short burst (about 1 second) of fluid into carb throat (or as close as possible behind baffle C) and promptly pull starter cord.
If engine fires and runs for a second or two then its a fuel/choke problem (compression is ok). If doesn't run, then more likely no spark but could still be a fuel or compression issue.