A single click followed by silence almost always points to one of three culprits: a dead cell in that new battery, a corroded ground connection, or a stuck starter solenoid. Most people jump straight to "bad starter motor" but that's usually wrong - a truly seized starter would either click repeatedly or do nothing at all.
Here's what everyone seems to overlook: check your ground cable first, especially where it bolts to the engine block. On older Yamahas, that connection gets corroded from the inside out, and a brand new battery won't overcome a loose ground. Unbolt it, scrape the connection point clean with a wire brush until it's shiny metal, then torque it back down. While you're there, trace that cable to the frame and make sure *that* connection is solid too. I've seen people waste hours chasing electrical gremlins when a ten-minute ground cleaning fixed everything.
If the ground checks out, pull the starter solenoid relay (check your manual for the location - usually near the battery) and rap it a few times with a wrench handle. Sometimes they just stick, and a little percussive persuasion frees them up. After that, if you're still getting the single click, you can swap the relay with another one of the same part number to test it. Only after ruling out the solenoid and ground should you assume the starter motor itself is gone, because that's a much bigger job on most bikes.