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.
"No, no, I don't mind being called the smartest man in the world. I just wish it wasn't this one." -- Adrian Veidt/Ozymandias, WATCHMEN