The Norton icon likely disappeared from the system tray or task bar because you are running different versions of Norton 360 within your Norton account. There are three different versions. You need to be running the latest version on all the machines on your MyNortonAccount.com account.
1. First, open your Norton 360 and click on "Help & Support" and then "About". Write down your serial number. You might need this later.
2. Run the Norton Removal Tool. http://www.symantec.com/nrt/
3. Then download Norton 360 Version 3. http://www.norton.com/n360s_3
This process may take 15 minutes or so, so make sure you allow plenty of time.