Zone Alarm is a firewall, but you mentioned Symantec, so you must be using Norton, rather.
It may be your culprit, since you 're able to connect in Safe Mode, where Norton is not loaded, yet.
This is what I suggest...
Download Norton Removal Tool:
http://service1.symantec.com/Support/tsgeninfo.nsf/docid/2005033108162039Physically disconnect from the internet (disconnect modem's cable).
Uninstall Norton, using the above tool.
Turn Windows firewall on:
Go Start>Control Panel. Double click on the Security Center icon. Click on the Windows Firewall icon beneath the status updates. Click On, then OK.Reconnect modem's cable.
Restart computer in Normal Mode, and see, if you can connect.
We'll go from there.