Do you enjoy other types of art? If you do, and can describe what you like about that, perhaps we can suggest particular music that might appeal to you.

If music doesn't resonate emotionally with you, there is also intricately patterned music that appeals to me in a more mathematical way. Bach's fugues, particularly his "little fugue" in G minor, are a good place to start. Following along with the sheet music may help with appreciating the clever ways in which the different voices relate to each other.

As for appreciating music emotionally, I find that it is necessary to relax into a certain mildly altered state of consciousness similar to meditation; I've become better at this over time, though I can't always do it when under stress. I've also heard numerous reports that marijuana aids in the appreciation of music (in a lasting, not a temporary, way---you notice new things in music that you can then continue to appreciate while sober), and will have to try it sometime.