Not sure what OS you're using but should be similar for XP/Vista.
1. Right-click on your clock in the task tray and click 'Customise notification icons'.
2. Make sure all icons have the behaviours set to 'Show notifications and icons' or 'Only show notifications'.
If this is already the case you may want to do a quick scan with Malwarebytes Anti-Malware. Should pick up any malware, spyware, adware, rouge AVs or irregular/malicious registry keys.