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:9.0.114.000
TrueVector version:9.0.114.000
Driver version:9.0.114.000
Anti-virus engine version:8.0.1.33
Anti-virus signature DAT file version:995793696
AntiSpam version:6.0.0.2383
ZoneAlarm ForceField 1.5.36.15
ZoneAlarm ForceField Spyware Scanner 1.5.53.22
ZoneAlarm ForceField Anti-Phishing Database 1.2.104.0
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?