Yes, it can. But, I doubt it will. If Norton gives an option to uninstall directly from the Start menu, do that. If not, use Add/Remove programs. It is generally the Symantec software that gives the problem.
What happens when you run Check Amazing Charts in the Amazing Utilities? What error message do you get? Also, with that big rectangular error message, doesn't it give you an option to let the virtual IT guy fix things? You know, run down the list and have it check setup or whatever and port and firewall, etc.
This should be rather easy to fix. I wouldn't assume Windows Firewall is off. It if isn't turn it off for now. You definitely don't want two firewalls running. You are better off with none to be honest (if you have a hardware firewall -- which you probably do if you have a router).
BUT, I WOULD DO THESE STEPS QUICKLY, THEN REMOVE NORTON 360 NOW. AS FAST AS YOU CAN. GET IT OFF THAT MACHINE. GUARANTEED TO HELP. IT'S AN INTERNET OR FIREWALL SUITE. THEY CAUSE THESE ISSUES. PLEASE UNINSTALL IT! You can always reinstall.
Also, and don't take this personally, but XP Home is for HOME, not work. In the future, do NOT put XP Home on your WORK network.
I bet with these steps and with Indy's help, you will be up and running today.
HTH