But computers don't take up nearly as much space. You would only need to shield that one specific spot where the computer was rather than the whole cockpit.
Yes, every particle crossing the copper can create an anomalous signal that can switch a 0 to 1 or visa versa. If you have enough of those, the program(s) will eventually crash. On the processors themselves the L1/L2 caches are vulnerable, but beyond that, the ROM could also get corrupted making hard resets impossible even after a crash.