I don't remember quite well the ICON starship combat (will have to dig my old books) but I guess the answer, based on what we see on screen, depends on how desperate your crew is
I would say that the most important systems are the shields, weapons, life support and computer. Anything else could be sacrified if the ship is in really big trouble. Maybe in desperate cases, even life support could be temporarily shutted down (the crew certainly prefers to float around not breathing much for a while instead of being vaporized).
"The main difference between Trekkies and Manchester United fans is that Trekkies never trashed a train carriage. So why are the Trekkies the social outcasts?"
Terry Pratchett