To see the status of a computer, do the following:

1. In the Symantec Management Console, click Manage > Assets.
2. In the left pane, under Assets, expand Manage Configuration Items > Computers and Peripherals, and then click Computer.
3. In the Computers list there is a column Status.

You can also go into Resource Manager and find the status on the left hand side in the Resource Associations.

In Case you need report to Check the Status of all Assets (Only If Asset Management Solution is installed)

Reports-->All Reports-->Service and Asset Management-->Assets -->General Asset Report

You can select Computers from drop down to check the Asset Status, Option is available to check the status and details of any asset.