I would suggest that you inspect the battery terminals and ensure that they are clean. The solenoid does not take very much power and the click which you can hear is likely to be the solenoid pulling the starter contacts together but, with a less that clean positive terminal, on the battery, the large amount of current, required by the battery, cannot flow. As someone has advised, some starters have a solenoid/switch where the starter contacts can be cleaned or replaced.