What happens when someone does not demonstrate Emotional Intelligence in the work place?

It really depends on the job. If you are a scientist, mathematician, or engineer, then emotional interaction, reading the inflections and body language of others, and so forth are not as critical.

If you are in a public-facing or people-oriented field such as public relations, communications, or marketing, then a lack of emotional intelligence will likely result in a very limited career.

In any case, emotional intelligence allows for a person to read others' emotions, adapt to emotional stresses, react properly to people within the context of collaboration and tactful interaction, and work with others in an effective and efficient fashion.

More and more, these skills are becoming critical as pressures in the overall job market require overlapping and interdisciplinary skill sets to collaborate for business goals.