FIXED!
Many thanks to
camstone
talvinamarich and especially
theweaselking for your help and suggestions.
james_b pegged the problem: MAC filtering for WiFi security. I'd forgotten to add the new PC MAC into the list.
Thanks everyone. Time for a quick snoopydance, then back to work.
Thanks everyone. Time for a quick snoopydance, then back to work.

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*grins*
Configuring XP is...is...I lack the words...actually I don't, but you don't want to hear them....
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New PC screams along.