Can't access remote sites on port 10000 with WinXP/2K

I have two remote Linux servers (two towns away) that run Webmin, an
administrative program that runs over the web on port 10000.

You access it by saying "https://the.server.com:10000" (note the "https").

I am able to access both of them from here on Linux but not on Windows...
if I enter "https://the.server.com:10000" into either MSIE or Firefox, it
just hangs for a while and then times out.

I can go to a DOS box and say "telnet the.server.com" and it works, but if
I say "telnet the.server.com 10000" it won't connect. However if I say
"telnet the.server.com 10000" from Linux it connects.

Something in Windows is blocking port 10000.

I have the Windows firewall turned off in XP, and 2K has no firewall. My
DSL firewall is turned off (temporarily, to try to isolate this problem).

The Linux boxes which connect OK are on the same subnet as the Windows
boxes that don't... in fact one of the Linux boxes is a VMware virtual
machine that is hosted on one of the WinXP boxes that won't connect, i.e.
the host won't connect but the Linux virtual machine will connect.

Like I said, something is blocking port 10000 on the WIndows boxes, and it
ain't the firewall. How can I fix that?