As AMB says, sounds like the starter relay is at fault. Check the terminals are tight as AMB suggest
One question to clear up though alrightnow. You say that when you press the starter button, the fuel pump primes and the relay clicks?
The fuel pump should prime when you first turn on the ignition, not when you hit the starter button. You'll hear a whirring noise. Can you confirm this happens.
If it does, then when you press the starter button you hear lots of clicks then it's a faulty starter relay or battery and as you've replaced the battery then it has to be the starter solenoid. You can double check by turning on the ignition and quickly bridging the 2 starter solenoid terminals with a screwdriver. You'll see a few sparks but if the engine turns over you've found the fault. Replace with a Yamaha solenoid. Part number 4KD81940-00 about £29 from any yamaha dealer