TRX300FW won't start, just clicks!!!!

My neighbor is a 90 years old woman who is somewhat crippled and uses her ATV to get the mail and see her farm.
It will not start and I have no way to get it to a shop but I am handy enough to do most any repair.
There is a round device in the battery case left of the battery that clicks loudly when I try to start the ATV.
What is this and does this sound like the problem.
What is necessary to replace it other than a new part.
Thanks For your help,
Pat