I'm having the same problem with my Craftsman Model #917.273764 Is there an easy way to determine if it's the starter motor or something else?

Have the battery load tested... new doesn't mean good, especially with cheap batteries.

Check the pos connection at the battery and at the solenoid.

Check the neg connection at the battery and at the chassis ground.

Sometimes the high voltage cables corrode up inside the insulation and it is hard to see.

Agree about having a 3 year old battery tested, since after 2 years, they are getting suspect.

You can do this test first however-

Jumper the 2 big terminals on the solenoid together, which bypasses the solenoid.

IF the engine cranks, the solenoid is bad.

IF it doesn't, weak battery, bad connection or bad starter.
A bad connection can include the engine mounting bolts which ground the engine to the frame.

Ooohhh, yes, many new starters are sold to poorly informed newbies, because of related problems with other parts of lawn equipment!
Take Bill Kapaun's advice and test the things he said to test, first. And make sure you connect the cables to the battery correctly!! Get them backwards, and the starter will spin backwards! And not start the engine.