OK, turns out that Mcafee was causing the problem. Probably the proxy service it runs. I disabled most of the services at first. Looks like Windows update is working.
.NET framework 1.0 was wiped out when the HDD failed. I copied over the entire directory from my Win XP Pro laptop and seemed to have fixed that problem.
Whew! .NET framework 2.0 just installed correctly from the updates.
Office 2003 is crippled at the moment. Word and Excel work, but Outlook does not. I need to repair the install....
The BSOD that started this (along with the HDD failure) was:
process1_initialization_failed
What a nightmare, but at least this WinXP install is on the road to recovery.
Normally, I would tell the person, that I need to format/reinstall and then dump the data back, but this is family and I like a Microsoft OS challenge

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P.S. It was the Mcafee proxy service that was causing the problem. Disabled, web pages load fine.