[Sorry (kinda-but-not-really) for the book: It's an important subject for me, personally.]
Kinda like what Danny said, If you don't exercise something it will atrophy. This is axiomatic for any "muscle" type, be it physical, mental, emotional, etc.
Stop exercising, your capacity for physical activity will diminish.
Stop using a language, your facility for that language will decrease.
Stop exercising your emotion, it will become more and more difficult to feel.
Emotion is the *only* motivation. It is only to the extent that you care about something that you are motivated to make progress toward that end. "apathy" means "without feeling" (a + pathos). So, if one is apathetic towards something, one will not do it.
I had a really difficult Jr High. I was a grade ahead, which meant I was a year behind. I got extremely proficient at turning my emotions off, because if you don't react they will get tired of messing with you. However, that resulted in a fairly comprehensive emotional flatlining that's taken almost two decades to overcome.
Different people are definitely born with varying levels of emotional capacity, but the constant is that we all have that capacity... and also that we never lose that capacity. Not eating much over a long period of time will cause your stomach to decrease in size, but you can increase it by practicing the inverse. It will take some time and the progress won't change overnight, but over time the effort will yield the desired results.
I don't know your story, and I don't claim to be anyone more than an observer and appreciator of people. However, I would venture a guess that difficult circumstances led you to choose to stifle your emotional output.
Often, a remedy for something is its opposite. To combat indecision, decisions must be made. To combat distrust, the choice to trust again is required. To combat emotional disconnect, we need to choose to engage our heart. Because emotion is an intangible thing and there's no system of metrics to measure results it can be difficult to perceive any progress.
I believe Danny had some good suggestions: Get out of your routine, get uncomfortable. Volunteer and purposefully involve yourself in the lives of others. Also, find people who have what you are looking for. Something that has helped me personally was observing and emulating my wife's hope in things. And not the macro, but the micro. Along with my emotional flatlining came my ability to manage my expectations: I simply chose to not ho[pe. I took what came and a lot of stuff just rolled off my back; it took a lot to crack my shell. However, the corollary was that it was very difficult for me to get excited about anything.
As with any resource, you can't get a return on something you didn't invest. I chose not to invest my emotions, so I didn't feel any. My wife, however, invests emotion into everything. One one hand this opens her up to disappointment, and she often is. However, she routinely gets much more excited about a good meal or movie because she chose to invest that emotion and allowed herself to hope that what she desired would come about.
You may be apathetic about much, but you are aware of this and you don't like it--which means you feel something, there. So you have a foundation to work from.
tl;dr version:
Muscles atrophy with disuse. Emotion is a muscle. Hit the "gym" by allowing yourself to hope for desired outcomes and by putting yourself in new, different, and likely uncomfortable situations. Emotional output can't be empirically measured, so there are no success metrics. However, emotion will unavoidably increase as it is exercised.
Take heart, hope, and don't go it alone.
