I've been thinking hard about that Faraday's cage, but what if someone needed to use the computer ? Also, the laptop wouldn't be trusty, so you never know exactly what's inside, what could emit information through any network. This would be really helpful in case of audit works, to prevent industrial spying for example.
Put it in a locked room in the basement, remove the hardware that it could use to attach to a network (cat-5 cable, wifi antenna, use a UPS that isolates from mains). Now you have to limit the users ability to attach to some network through the exposed UI, I'd suggest a guard in a separate users room as shown in my previous answer here.