OK,

I decided to take apart the connector. The blue part was just a
plastic holder. Inside were 2 metal pins hooked to each side of the
cable. For lack of a better term, they were basically stappled into
each of the two "wires". Seeing how it was connected, I got
inspired. I bought a connector like you see at the end of an IDE
connector. This one had 8 pins, so I removed 6 of them. I cut off
the wire and discarded the portion with the hole in it. I was able to
punch the pins through the wires just perfectly but it still didn't
work. So it's starting to look like there is a problem somewhere else
in the wire.

Since getting taking the wire out would involve literally hundreds of
screws, I'll wait till I have to go in the keyboard for some other
repair. I guess I can live with it for now.

Thanks to everyone for their great advice.

Francis