Small Engine Troubleshooting Problems? Ask a Mechanic Now.
425 is carburetor engine. If you remove a spark plug and ground it, do you have spark? If you have spark, put teaspoon of fuel into the spark plug hole, re-install the spark pug, and see if it will start for a few seconds.
If it does, check the solenoid in the carburetor, it has to open the fuel passage to the cylinders. It should click open as soon as key is turned on. Has to have 12 volts at all times key is on.
With twin engine, you have duel coils and pickups, and a single igniter. So if no spark on either cylinder, the igniter is questionable.
Did you get chance to check the mower?