Norton can be a real pig to remove so I would advise you follow the steps Tech gave in the other post to ensure it is completely removed.

You mention that you have avast on your other computer and that works are there any differences in the installed software, e.g. did you also have NAV on that system ?

If after using the NAV removal tool you still have this problem (but I suspect it may resolve it), check the windows firewall, does it have an exception for ashWebSv.exe ?
Although I mention this I’m none to hopeful as the windows firewall doesn’t have any outbound protection and I would suggest you get a third party firewall that does.

Whilst the windows XP firewall is usually good at keeping your ports stealthed (hidden) it provides no outbound protection and you should consider a third party firewall.

Any malware that manages to get past your defences will have free reign to connect to the internet to either download more of the same, pass your personal data (sensitive or otherwise, user names, passwords, keylogger retrieved data, etc.) or open a backdoor to your computer, so outbound protection is essential.