TMI wasn't caused by a computer failure but the accident was made vastly worse by an error of computer design. Specifically, TMI-2 had a terrible user interface.
See, See. UI is important!!!!
I'm a nuclear engineer and I think the use of the term UI for the control room is somewhat 'simplistic'. I personally think a major issue was over design in a certain area (redundant alarms), and lack of safety systems that would prevent the core from melting even with a LOCA in place. It was two hours after the shutdown when the fuel melting began at TMI-2. This was a scenario where the operators couldn't understand what was happening. Now from an operator's perspective (who sits in the operator room) you're not looking at a "UI" in the traditional CS sense. Here is an image of a control room: http://www.ornl.gov/info/ornlreview/v38_1_05/images/a11_controls_full.jpg The events leading up to the disaster started on the secondary side (non-core) leading to a LOCA (Loss of Coolant Accident). For those unfamiliar with the term "secondary side". The secondary side of a Nuclear Power Plant is similar to that of any power generating plant, meaning the secondary side does not contain the reactor core.
"The Avis WIZARD decides if you get to drive a car. Your head won't touch the pillow of a Sheraton unless their computer says it's okay." -- Arthur Miller