I worked in IT plus I’m a 1980’s era computer nerd so I do believe it was quite doable to have such a system. I also talked to an older co-worker who is in his 70’s, he worked for Fairchild on the early guidance computers the military used on F-101’s and F-102’s where the pilots wore the computer box on their leg and plugged it into the plane. He told me that it really did not require lots of computer power to search, assess, select and guide a missile to target so the boxes had like 4K to 8K of RAM memory to them. We went to the Moon with the same amount of computing power, maybe a little more like 16K plus the needed programs in ROM memory. I do believe it could have worked, at least the land based laser/particle beams, the limiting factor is how fast you can charge them up to fire again.
today youtube has multiple videos of people making experimental railguns in their garages.