Shimano dual lever Ultegra ST-6600 The shifter cable broke on the way home from work. The break was inside of the dual lever assembly. I was able to fish out the cable end. But, with a new cable, I am not able to get the shifter to work properly.

Any tips on dis-assembly and re-assembly of Shimano dual levers? Specifically, 
ST-6600. I found the techdocs on the Shimano site, but rather obtuse. Tips appreciated.
My tip would be don't disassemble the lever! Shimano unfortunately did not design their shifters to be serviceable.
Shimano STI levers had a terrible habit of fraying the cable at the cable head until it eventually broke off. This was supposed to be remedied in the new generation of shifters but they still do it to a lesser degree. In other words, you're not alone in this problem. 
Unless you broke something while fishing the cable head out I'd say there's good chance that there's still a piece of cable floating around inside the shifter somewhere. My suggestion would be to undo the brake cable so you can pull the lever further back and get a powerful flashlight to look around inside the shifter with. Actuate the shifter and see if you see anything amiss. The whole thing would be easier if you take the shifter completely off the bike.