You can get a clicking sound if you either have bad earths or connections on the main leads - even with a new battery. Corrosion builds up on the cables and then you don't get full power. With a weak battery you can also damage the solenoid so even with a new battery solenoid will only click.
Check all leads are clean and tight on connections to both battery and earth to chassis.
If that all checks out okay change solenoid.
epark mowers
April 2011