Since the repair shop apparently looked at the mower why didn't you have them do the work? That's usually a better and less costly way to repair than just swapping out parts.

Did the electric start work before the battery was changed? If so check the battery terminal connections to make sure they are solid and clean. Next thing to check is the condition of the battery. Does it have a full charge? If that's ok then check to be sure the ground strap is secured.

I'll say it again - you might want to have the repair shop do the work.

The starter motor is the last thing I would suspect because it's probably the most reliable part of the system. Did I mention that it's the most profitable part sale for the shop? Oops, sorry about that.

Check for voltage at the terminal that attaches to the starter body when the key is turned. If no voltage there, look for any loose connection, malfunctioning lever, keyswitch or battery.

If you have voltage at the red terminal on the starter, I would look at the starter itself.

There would be a 40AMP fuse in the battery box and a microswitch on the control where the zone cable meets the engine. Sometimes the terminals get pulled out of that switch or simply a wire gets pulled off.