How will you check if router goes down?

Every router has a LED to indicate whether the connection to the internet is healthy/not.
If the connection is healthy i.e. smooth n going.... then the LED glows Green
If the connection is unhealthy i.e. the router goes down / there is some disruption in the n/w path.. then the LED glows Amber (Yellowish Orange)

by connecting console cable to pc and using Hyper terminal logging in router ,check the logs other wise the router gets restart often.