OK, I have isolated the bug, further.  I have removed the slave 200 Gig hard drive, (it was just extra storage) a USB 2.0 PCI card, and the scanner to reduce psu overload.  I have also unhooked the master dvd burner, further reducing power usage.

I then hooked up the slave dvd burner as a master (cable select jumper) and fired up the computer.  My first attempt to back up a movie with dvd shrink, 
the preview box showed the jerking around that I've previously described, 
and the timer indicated that it would take 1 hr. 10 min. to back-up, 
preparatory to burning.  

I then shut down and rehooked up the same burner, using only the slave 
connector on the ribbon cable.  That was the only change I made.  I re-tried
dvd shrink, and this time the video screen showed smooth and rapid back-up, 
and the timer indicated that the movie would back-up in 15 minutes.

Anybody know what the heck that means?  As a pure wild guess, does that mean 
that the area of the cpu that handles the master traffic from the secondary 
IDE interface is going bad?  (Hoping I used correct terminology there.)

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