I've been trying, unsuccessfully, to diagnose the no-start issue with my mower; Murray 425009x8A with B&S 31R907-0007-G1 engine. It died while I was mowing.
The flywheel spins and I can get it to run at 1/4 power for a second or two. I've been assuming that a bad switch would be like disconnecting the battery, preventing the flywheel from turning. Is this a correct assumption.
Thus far, replaced the carb, coil, plug and gas.
Fresh fuel, fresh air, good spark & good cylinder compression are needed to run. Use OEM B&S & Murray parts.
See Wiring Schematic page 10 in Parts Manual above, use multimeter or 12v test light to troubleshoot electrical system.
Safety switches interrupt the starting circuit so nothing happens when one of them is triggered , some are normally open and some are normally closed. If your machine is spinning and trying to start , it's not a safety switch problem
yours sounds like a fuel issue, shoot some starting fluid in the carb while spinning over , if it hits and tries to run ,it's pointing to fuel - if not ,,, spark.