Resolved Srvr2003: WindowsUpdate will not complete...

I need assistance in troubleshooting a specific problem with Windows Update on 32-bit Server2003. I've verified that proxy settings are correct, and are identical another server2003 system on the same subnet, which works perfectly, so the problem is going to be in Server2003, rather than the network.
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On the machine that works:

1.) Windows Update checks for the proper version of Windows Update components. 3-4 TCP connections established to the proxy.
2.) Windows Update shows the screen with the buttons "Express" and "Custom ".
3.) I click the Custom button. The same 3-4 TCP connections are open to the proxy, for the 1-2 mins it takes to do the check, while "Checking for Updates..." is displayed on the screen.
4.) WIndows Update finishes, and displays a list of the missing patches on the screen.

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On the machine that does NOT work:

1.) Windows Update checks for the proper version of Windows Update components. 3-4 TCP connections established to the proxy.
2.) Windows Update shows the screen with the buttons "Express" and "Custom ".
3.) I click the Custom button. The same 3-4 TCP connections are open to the proxy at this time. "Checking for Updates..." appears on the screen. After ~3-4 mins, the TCP connections to the proxy come out of ESTABLISHED state, to TIME_WAIT. After 5min, the connections time out entirely, and there are NO connections to the proxy. NOTE: "Checking for Updates..." is still displayed on the screen, and [will] stay there forever & nothing ever happens.

Question for pondering: What is the broken system *supposed* to be doing that it's not doing, and allowing the TCP connections to the proxy to age out & disconnect?

 

OP here: Significant difference in how these two systems do their updates. I looked at c:\windows\windowsupdate.log, and the machine that works, is always talking about "MicrosoftUpdate ", whereas the machine that's not working, is always talking about "WindowsUpdate" in the logs. Plus, I notice that we always see a link, "Upgrade to MicrosoftUpdate today!!!" on the machine that doesn't work -- this does not appear on the machine that works. Apparently the non-working machine is still using the older WindowsUpdate....

 

Indeed.. This is a situation where I work -- I'm the guy who helps the people who take care of the machines -- I'm not supposed to do the work myself; others are responsible for that. --I've already suggested to the sys-Admin of this paticular machine to move it to MicrosoftUpdate from WindowsUpdate.