Firefox is acting very strange, please read carefully

I have installed Win 7 Home Premium 32 bit , I am also running Zone Alarm as below:

ZoneAlarm Extreme Security version:
TrueVector version:
Driver version:
Anti-virus engine version:
Anti-virus signature DAT file version:995793696
AntiSpam version:
ZoneAlarm ForceField
ZoneAlarm ForceField Spyware Scanner
ZoneAlarm ForceField Anti-Phishing Database
ZoneAlarm ForceField Spyware Sites Database 03.980

When I start Firefox normally I cannot connect to the internet. However if I right mouse click on the Z in my task bar and then click on either start unprotected browser or start private browser it works fine. If I click on simply start browser, that session of Firefox will not connect to the internet.

Any ideas?