Yes, take the new one off and test it. Also, take the push button assembly off and run power directly to the stud sticking out of the starter housing. What is the voltage at the battery posts while the start pedal is being pushed? (This takes two people- - -one to operate the pedal and another to measure the voltage.) It's remotely possible you've got an open circuit internally in the battery- - - -even a new one. It will show normal no load voltage and then drop to zero as soon as the starter load goes on it. Make this test directly on the posts- - -NOT the terminals bolted to them. Then repeat the test with the voltmeter connected to the cable terminals, not the posts. If the voltage is good at the battery and drops at the cable clamps- - -clean them!
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
Love your enemies and drive 'em nuts!