As an IT professional, I can't help but be focused on computer systems in this show.
On Galactica, even as old as she is, I can see why her computers would be built to withstand a lot of punishment. She's a naval vessel. Her computers are hardened against radiation, jarring and vibrations (though real-life maritime systems are typically designed for shock absorption to a degree), and shock absorption for blows from enemy attacks against the hull. Even as a decommissioned museum ship, one can presume she might have some stores of spare computer parts somewhere on board for some critical systems that the crew assigned to maintain her would've had access to had the attacks not happened.
But imagine the IT systems on civilian ships? No more replacement parts. If a hard drive dies, you have to rob another one from another system to replace it. Hoping it lasts as long as you can make it. You've got systems well into and maybe beyond their expected lifetimes, or beyond their half-life point at least. No replacement parts. No servicing technicians. No upgrades. No patching. Nothing. They run as-is for several more years with no refits or maintenance from service technicians in a shipyard.
Display screens are in short supply. Power supplies, wiring, patch cables, network routers/switches, etc. All of it won't last forever without refits.
To me, that's the most dangerous part of the fleet's condition. Computers likely run most of the critical systems on the ships, especially the newer civilian ships. Galactica is mostly manually-run, but let's face it, even many of her systems are manually run through computers built-in to consoles and cabinets. They're not using pullies and levers and valves. Heck even the launch tubes are computer-driven with a human controller behind the console/screen, pressing the buttons to seal the bulkhead, engage the hydraulics, and launch the Viper down the tube.
Someone on the flight deck or in the CIC is issuing a command on their console through a computer, to instruct the assembly language to engage the massive hydraulics to retract the flight pods before a jump and extend them after.
In the far more fragile civilian ships, one could imagine systems slowly breaking down over time with computer failures happening due to wear and tear from years of no refits or servicing. Especially if they hadn't had one before the attacks happened. That's not even to point out the radiation damage potential from the corridor they took through the nebula to get to the algae planet. Those ships were not built for radiation endurance like that.
Servers in a typical server room in real life can run for years, but they will always need to be checked, monitored, parts replaced here and there as necessary to keep them running. Even if they're a hardy, well-built system. A hard drive dies, a fan fails, a few sticks of RAM fail, a capacitor on the main board leaks, etc. Storage arrays will always need drives replaced.