I was able to capture a "before" clip on NBC news and an "after" clip from the Jim Lehrer News Hour on PBS.

The clips show an interview with the girls and explain the nature of the surgery involved (and what went wrong).

I've edited them together into a single news reel:

NBC and PBS On The Conjoined Twins. (Small - 6 MB)

So they died from blood loss -- most likely when the makeshift grafted brain arteries didn't hold. Perhaps they should have waited another couple of years. (When we will be growing arteries whole :)