A nuclear detonation produces a huge surge of electromagnetic radiation across the entire spectrum. The lower the wavelength, the farther the EM radiation travels, so microwave and radio are what would concern you, since if your computer is close enough to need shielding from X-rays and gamma, protecting your processor would probably be less important than, say, extinguishing your house. Good materials for shielding Radio Frequency radiation are steel, brass, and silver. Here is a link if youre interested:
http://www.thermaflo.com/rfshields.shtml
Nuclear detonations also produce a large magnetic field, like how your speakers have a magnetic field. Magnetic fields also cause electrical surges (generators use spinning magnetic fields to "pump" electrons). Good materials for shielding from magnetic fields are iron, steel, and anything else that a magnet will stick to. These materials are reffered to as "permeable". In this case, you arent so much blocking incoming radiation as you are letting the permeable material soak up the field and divert it around your computer. Here is another link, this one to a site offering magnetic shielding:
http://www.advancemag.com/
It has some really irritating midi music playing so turn down your speakers before you go there.
Finally, Nuclear detonations release a lot of Nuclear Radiation, which is different from the above two types of radiation. This is where Neutrons, Protons, and Electrons bust loose from a decomposing atom and fly away at high speed, smacking other atoms and altering them chemically. Alpha and Beta particles arent really a threat to your computer because they generally cant penetrate much more than a sheet of paper, but Gamma particles (neutrons) take a hell of a lot of lead and other dense materials to stop them. So you would constantly have neutrons literally whizzing through your computer and smacking atoms in your ram and hard drive platters and occasionally changing 1's to 0's and your data would get all corrupted and your computer would crash frequently. Go here to learn about Nuclear Radiation:
http://science.howstuffworks.com/nuclear.htm
I highly reccomend
www.howstuffworks.com in general for learning about things.
So, in summation, I posted this mainly for academic purposes. While you CAN shield your computer to some extent, maybe even enough to keep it working after some kind of detonation/accident so long as the event occurs far enough away, its really just a matter of degree. You can not 100% shield it from something happening 20 miles away or less, but if that happens you really have bigger problems.
Im sorry, I know my grammar is atrocious but its 5:52 am and I havent slept yet so I ask that you forgive me. =p