Intelligent Design basically says that if a thing, a cell for instance, won't work if only one component is taken away.
You are describing Irreducible Complexlty, not Intelligent Design. Irreducible Complexity is the falacious idea popularized by Michael Behe which has been used to support the idea of Intelligent Design.
A little more on irreducible complexity. Basically part of the idea is that IF complex structures such as the eye or the ear evolved SLOWLY, piece by piece as evolution proposes, it would take a long time (many generations) for any benefit to the organism.
So if natural selection causes the better equipped to survive and thrive, why was the partially completed and non functional organ genetically transmitted from generation to generation until it was complete, when in the mean time it did the organism absolutely no good, and in some cases harmed it?
For instance the idea of a jawbone shrinking over time and becoming one of the bones of the inner ear-- how did the many generations of hapless creatures eat with a shrinking jawbone or hear without a fully developed ear in the mean time?
This problem is recognized by evolutionists, but their faith is strong. It MUST have been so. As in this quote:
Exactly how therapsid and early mammal ears functioned is not clear. A remaining problem concerns exactly how the transition from a tympanum in contact with the stapes to a differently-oriented tympanum contacting the malleus took place. One authority has suggested that for a time, there may in fact have been two tympanic membranes, the old one located towards the back of the skull and touching the stapes, and a new one located more anteriorally and on the outside surface of the lower jaw, touching the reflected lamina of the articular (Allin, 1986). There is little doubt, however, that such a change took place; not only is it clear from the fossil record, but the sequence of changes from an articular-quadrate joint to a dentary squamosal joint with the articular and quadrate participating in the middle ear can actually be seen in the developing young of opossums.
Thus, the development of the middle ear of mammals and the their single-bone lower jaw are part of the same package. Why might these changes have occurred? We don't know, but we can speculate. And what follows is indeed speculation; we probably cannot know the answer to this question.
Irreducible complexity also is an issue at the level of cellular life. Before the first living cell could survive, it's sub-component parts must be present and functioning. The idea that sub-components of the cell formed themselves first and functioned without the support structure of the entire cell and patiently waited till the other sub-components also formed and then all sub-components joined together in a magic moment is just too funny for words.
(Also if you put sub-component parts of a cell singly into the same type of chemical environment from which they supposedly sprang and they will be chemically degraded in short order. They won't be able to wait around till other sub-components get their act together to form a cell.)
The cell's DNA, as an example:
But the major problem is the origin of the genetic code and of its translation mechanism. ...... The code is meaningless unless translated. The modern cell's translating machinery consists of at least fifty macromolecular components which are themselves coded in DNA: the code cannot be translated otherwise than by products of translation.
In other words, the cell needs DNA to be successfully decoded to tell it how to build the components that will successfully decode the DNA.
Irreducible complexity simply states the obvious, that to be useful to an organism some substances or structures are dependent on the presence and function of others. The idea that these things appeared singly, one at a time until all were present and VOILA they all started working together is completely illogical.