Well, to answer the question, "Who defines the problems?" Society tends to in the end. Engineering tends to follow - if not worship - money (its the mother's milk of more than politics 'ya know), and at some point, putting up the money for the solution is a social/cultural deal, not an engineering deal. And the end decision - to adopt or not - is never an engineering solution, its always a social and cultural decision.
That's why solutions exist that are not put into practice.
The Greeks had steam power. They used it for a trick or two, like opening the doors to the Temple at Delphi when one went to see the Oracle. But they never sought to apply that power on a more widespread basis, saving labor was not in the best interest of a slave culture. Keeping slaves busy - not idle - is in the best interest of a slave culture.
Or, try this one. The Chinese invented/discovered gunpowder. They used it to create one of the most beautiful technological things in the history of the world, aerial pyrotechnics - fireworks to the layperson. When the Europeans saw them, their first thought was, "hey, lets use that to kill people" and promptly invented the gun and the cannon. A society like China, one that valued harmony and stability had less than zero use for a weapon that would allow a small group to equalize its numeric disadvantage with a larger group. Europe at that time saw it in just the opposite way.
Even the choice of what task a computer must/should solve is driven by market forces more than anything else. While Woz may have been a true engineer, looking for a way to make somethings work in a smaller and more user friendly way - it was the apps as it were (and two in particular, word processing and spreadsheets/accounting) that really drove the initial sales of personal computers by radically changing the way two basic business tasks were accomplished. Computers still are used for the basic reason they were invented - doing mass calculations - but to put on in every office, and then every home, required it doing something more than stress calculations or working though firing solutions for weapons (the original two uses). And while Woz and Apple deserve a lot of praise for what they did, Wang with its original word processing machines, and Lotus 1-2-3 deserve some credit for doing things that first business, and then ordinary persons wanted to do.
So while engineers 'solve' problems, they don't often get to define what the 'problem' to be solved is.
