There are two things you have to consider when talking about an "emotional" computer. The first is whether or not the computer, itself, has emotions, and the other is whether or not they understand human emotions.
We've already developed machine emotions. The common system management tool Nagios is specifically designed to poll the emotions of the systems under its care, and let the system managers know when the systems are distressed, overworked, bloated, bored, or suffering any of a number of physical maladies.
The normal response to this is "those emotions aren't human emotions, therefore they are not real emotions." This is a failure of flexibility on these people's part because they don't understand the role of emotions.
Emotions are a neurochemical shortcut for creatures to recognize problems before they can rationally understand them. We don't monitor our blood sugar and decide that it's time to eat, we just know that we're hungry. The downside of this is that the "hungry" emotion has a lot of noise to it, and numerous things can be mistaken for it. We fear things because a complicated biochemical pattern matching sends a signal to our brains telling us we need to be cautious, or even to panic. Anyone with PTSD knows that this is something that happens below rational understanding.
Machines are similar. They often don't know that their hard drive is experiencing pre-failure symptoms, but they will still know that their data stream is constipated. These are real machine emotions that serve the same purpose of human emotions.
Theory of mind
A machine is capable of modeling a human mind, and guessing how specific stimulus will make us react. Right now, the best we can do is to generalize this for advertising purposes, but we will inevitably get to the point where machines actually understand us in ways we don't even want to understand ourselves. This isn't the same thing as experiencing emotions, but it's a forerunner to such a thing.
This technology would use the previous technology to provide a machine with a starting point for rational thought. It initializes a theory of mind with parameters that it would apply to a human, then references that theory of mind when it decides what behaviors it "wants" to engage in. It would be silly to generate an irrational machine by initializing it with irrational beliefs, but I'm pretty sure that someone will do so just to try to rationalize, realize, or even enforce what they think is "real."