The importance of technology can be defined in many ways depending on the perspective of the person doing the defining. I would say the important thing about technology is its value to people who use the technology. So taking your building blocks I would put them in this order.
Competent people to manage the information: Without competent people everything else is superfluous.
Communication device: The need to communicate with technology or using technology for communication is the basis of good technology.
Input/output device: Easily getting the information into or out of technology is critical for propagation.
Processing engine: What value technology can provide is based on what it actually does with or to the data it collects / stores. Or what it does for the end users.
Software: As it relates to the above its functionality is critical. As it relates to the importance of technology on its own it has no value. e.g. Oracle vs. Microsoft vs. SAP ECT.
Storage device: If it stores enough that is important but that aside it is unimportant.
