In Battlestar Galactica, William Adama expresses his disdain for networks given how easily the Cylons can exploit them thereby crippling their systems. If there are truly no networks in use, then how is DRADIS possible? How is inter-ship communication possible? How is it even possible for each ship to monitor its own status? All of these things and more would rely on networks being established, would they not?
Yes, there are systems that ostensibly have to have a private network to make the ship run and display status in CIC, but each system is it's own separate, closed network.
Take the FTL drive system. There is a computer that calculates jump coordinates, a computer that controls the jump drive (these two may be the same one) and a display and key panel in the CIC. These three components are networked, but only with themselves. If the Cylons hack the communications system from outside they would not be able to access any other system from that because they are all separate.
This is why the backdoor that was in Gaius Baltar's software wasn't an issue for the Galactica. It could only operate in a fully networked environment, and because Galactica had no inter-networked systems the software wouldn't run and was never loaded into memory.
GAETA: So let me get this straight. You're saying that the Cylons found a way to use your navigation program to disable our ships?
BALTAR: Essentially, uh, yes. I think they're using the CNP to infect your ships with some kind of computer virus, which makes them susceptible to Cylon commands.
GAETA: Uh, well, you can see we do have your CNP navigation program here on Galactica, but... our computers aren't networked, so it's never been loaded into primary memory, or even test run.
He doesn't want networked programs. They don't object to humans talking over communications systems; they just don't want to allow the Cylons to properly use their advantage in the software realm. In the networked systems on other ships, a single vulnerability let the Cylons hack and disable all Colonial systems. The Galactica only had a few isolated systems compromised, and those were manually reset.
In real life, there's no reason to believe that the Cylons would be more effective at hacking human systems than other humans, except for the exploit they wormed into the code before the attack. Adama's worry was unrealistic, but in this particular circumstance saved him.
Galactica was also older technology, so it's entirely possible many of its systems used analog control techniques. When the first cars were built you could still turn the steering wheel and have the tires responsd - there was a "mechanical network" between the two. Later that became mechanical/hydraulic. Computer have entered into such things these days to varying degrees.
I actually had the pleasure of working at General Dynamics in 1982 as a bright-eyed college student, and learned that the F-16 set a new high-water mark as a "fly by wire" jet.
To apply this to Galactica, someone above mentioned the FTL system containing computers. But it MIGHT NOT HAVE. There could have been a wire from each one of the keys on the keypad directly into a control system for the thing that possibly contained no von Neumann style stored program devices.
Computers are a great way to control things, but they're not the only way.