An aircraft carrier with destroyed pumps, engines, everything, as long as the structure is more or less ok, will stay afloat. Wait... An aircraft carrier can withstand a nuclear missile, and then keep sailing (the people are going to be dead through). This was proved in the 50s (old tech baby) when the government tested nuking a retired navy fleet of carriers and destroyers to see if they will sink. They didn't understand radiation, but the ships still sailed home. 5% of the fleet was destroyed.
Lets look at the stealth bomber example as noted by btilly. While its true if the computer dies, the plane falls like a rock. However the pilot can still eject. The ejection mechanism is not linked to the computer except for maybe the automatic mode.
I think the two "worstly" engineered vehicles are airliners and helicopters. Small planes can land without power due to the aerodynamics and weight, as long as hydrolics work. Airliners are not able to glide so well, nor are they light.
Airliners though do still demonstrate the redundant designs, each critical system has a backup which is a completely different in both their physical location and approach to solving the problem. If one fails the other can take over because a completely different set of conditions will cause the other to fail.
I think Battlestar Galactica did a good job showing REAL engineering. Those ships took a lot of pounding before they got destroyed. The only time the battlestars were just easily obliterated (like the enterprise was in every other episode) is when they were hooked up with a new computer system that connected every part of the ship to itself (and the computer was compromised) this was in the very first episode. Galactica survived BECAUSE it had all of it's systems disconnected and redundant, so when some shut down, people took over operations of that one back in manual mode. Hell part of the plot was that galactica was being sabotaged. In startrek sabotage was "opse the ship is going to explode now" while in galactica they just had some damage, or had their fuel blow up, or something (can't remember 100% of the details) but point being that you can't just blow the damn ship up. Maybe a civilian ship, not the warship. The only stupid thing in galactica was the cylon battleships had that central column which was succeptable to being blown up and destroying the ship, and that resurrection ship which if destroyed would fuck up resurrection for an entire cluster. I would have expected redundant resurrection ships/hubs.
In any case, the most unbelievable part of this whole ordeal is that you have a very large ship, full of civilians, armed to the teeth, the damn flagship of the fleet. That is all. Since when does the united states (or any country EVER) pack their destroyers or stealth bombers with civilians? Preach all you want about "exploration", in a real scenario you would have a mostly unarmed science vessel armed to the teeth with sensor gear, and a warship next to it for protection. Hell maybe the science vessel docks in the warship most of the time. The second an enemy approaches, the science vessel is already in high warp with every bit of stealth engaged getting the hell away from there until the warship signals them that it's safe to return.