|Does the clicking sound come out of the speakers?|
If the clicking comes out of the speakers, it is likely a refresh tick that is made when internet explorer reloads a page. This could be caused by some malfunctioning software or a virus constantly communicating to a website.
To fix this, check what software is running and close any programs that you aren’t using). It would also be advised to perform an anti-virus scan to make sure that there is no malicious software causing this behaviour.
If this is not the case, then please post back how you connect to the internet (Dial-up/Broadband/LAN/Wireless).
Some wireless adapters can cause interference with speakers, which cause a rapid clicking noise that comes out the speakers. But because wireless adapters run all the time (scanning for new networks) the clicking would not stop when you disconnect.