After finding nothing, I decided to reconnect the motherboard with the
minimum hardware required to see if it would turn on.  At first I added
RAM, attached the display cable, the power switch, CMOS battery, and the
power lead from the power adapter.  No LED or any sign of life occurred
when the power switch was depressed.  I felt that should have been
enough to at least turn on the computer, but I thought I would add one
component at a time to see if more was required.  I then attached the
keyboard cable and tried it again.  The computer powered up.

Eventually I attached all the other cables and hardware checking it
after each was attached.  It powered up with no problems.  In fact it
appears as if I solved my computer problem with power not starting or
even lighting the power LED.  It has been working flawlessly ever since.

My question is this:  Does the lack of a keyboard on a laptop inhibit
the power from turning on??  I have worked on many desktop computers and
the lack of a keyboard generally produces an error message during POST.
  I have never seen one stop it from powering up.  I hate solving a
problem and not understanding why it behaved as it did.  My guess is
that a poor connection to one of the cables was the cause, perhaps the
keyboard.

        What seemed to be fixed as described above was not the case.  (The fact
that the computer started working had nothing to do with the keyboard
being connected.  It was simply a coincidence.)  The computer did work
for several weeks and I thought perhaps it had been fixed, even though I
did not understand how.  Suddenly it started displaying the same failure
symptoms that I originally encountered again.  This time before taking
the computer apart I searched the web to see if others with the same
model of computer had experienced a similar failure.  I found that many
had, and that many thought it was attributed to the power switch
daughter board used to turn on the computer.  Again I don't quite
understand the bizarre failures since they changed in their symptoms,
but I decided to look at the computer again with particular attention to
the daughter board used to turn on the power.  I looked for a poor
solder connection since intermittent failures are most often due to such
a failure based upon my experience.  I did not see any poor connections,
but I re-soldered all the connections I could before reinstalling the board.

        Again the computer worked and has been working for about two weeks.  Is
it fixed??  I am not sure.  It is working, and since there are others
that believe the power switch daughter board was the reason for their
failure, I thought I would pass on my experience.