to fix the secure sites problem, try the fixes mentioned here:
http://support.microsoft.com/?kbid=813444
the article is about winXP, so everything upto the last four steps is applicaple, but those will not.
Does it affect all secure sites or just some? if it is just some sites then it may be your proxy server, try specifying a differnet on in tools -> internet options -> connections -> lan settings. Try 62.255.0.5 on port 8080 because i know this one is working fine ATM.
IIRC the symantec site uses and ActiveX plugin; these maybe disabled in the internet options... check in internet options -> security -> custom level.
If there are problems with firewall/AV it seems like this is blocking new programs from accessing the internet, hence why mozilla cannot connect. Try uninstalling NIS again and then after a reboot run a program like reg cleaner. If everything is then working ok, try reinstalling NIS again.
hth
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