Basically, any error in the cell cycle signaling may cause the generation of a cancer cell, since this loses control of mitogenic signals and the phases of the cycle. As colleagues have well commented you, there are several kinases and transcription factors that are involved in cell cycle control (pay attention also to p53, pRB, E2F, cdc25....and others proteins directly related with cell cycle cascades) but the effector proteins will be, ultimately, which will suppress / enable the uncontrolled division of a cell. These effector proteins are cyclins / cdks, which form various complexes and regulate the entry into G1, S and G2.
Your question gives for a lengthy discussion, but I think the key points could be these.
In normal cells signalling is very tightly controlled. Many feedback mechanisms occur to keep the signalling routes in check and to switch them off. In many cancers one can see sustained signalling which can be caused by overstimulation of the receptors, but can also result from impaired switch off mechanisms. These not only affect the cell cycle as disused above, but can also lead to increased migration or invasion of cells and can affect the way cells react to chemotoxic drugs and give them an advantage to survive.
First parts belongs to cause of malfunctioning in signalling which can be due to ingestion of some toxic substances, bad habits, bad lifestyle and environmental reasons.
The Second part of question is more interesting to answer where every disruption or alteration in cell signalling always need not to transform a cell into cancer cell. However after several such unfortunate events can lead to the cancer and in that events altered signalling is just one event.
Moreover in signalling, kinase, nuclear transcription, and over expression of protein machinery abrupt increased.
Anyhow, the ultimate cause (the why) is a change in DNA somewhere, within the sequence of a signaling molecule, within the regulatory/promoter region of a signaling protein gene or tumor suppressor, the fusion of two genes, the insertion of a foreign oncogene that high jacks a signaling pathway, or something like that. As most people have pointed out, errors in key components of signaling pathways can cause cancer; however, these errors must be transmissible to the "progeny" of the cell, which implies DNA changes or mutations.